diff --git a/include/torch-mlir/Dialect/Torch/IR/TorchOps.td b/include/torch-mlir/Dialect/Torch/IR/TorchOps.td
index 65f514c2e..035632878 100644
--- a/include/torch-mlir/Dialect/Torch/IR/TorchOps.td
+++ b/include/torch-mlir/Dialect/Torch/IR/TorchOps.td
@@ -11,6 +11,7 @@
 #define TORCH_OPS
 
 include "torch-mlir/Dialect/Torch/IR/TorchTypes.td"
+include "mlir/IR/BuiltinAttributes.td"
 include "mlir/IR/OpAsmInterface.td"
 include "mlir/IR/SymbolInterfaces.td"
 include "mlir/Interfaces/CastInterfaces.td"
@@ -1337,4 +1338,67 @@ def Torch_DtypeCalculateYieldDtypesOp : Torch_Op<"dtype.calculate.yield.dtypes",
   let hasVerifier = 1;
 }
 
+//===----------------------------------------------------------------------===//
+// Symbolic shape modeling ops for TorchDynamo frontend.
+//===----------------------------------------------------------------------===//
+
+def Torch_SymbolicIntOp : Torch_Op<"symbolic_int", [Pure]> {
+  let summary = "Symbolic int representing a dynamic dimension";
+  let description = [{
+    The `torch.symbolic_int` operation captures a dynamic dimension on the
+    global function arguments as exported by TorchDynamo (torch.export).
+    It associates the shape symbols (i.e. "s0", "s1") with the
+    global SSA values (i.e. `%0`, `%1`) that is then referenced
+    to bind shapes on op results.
+
+    Additionally, the operation annotates `min_val` and `max_val` attributes
+    denoting the range constraints for the dynamic dimension. This may be
+    useful for modeling runtime shape guards, or compile-time optimizations
+    based on the shape bounds (min, opt, max) on results of ops / regions.
+
+    Example:
+    ```
+    %0 = torch.symbolic_int "s0" {min_val = 5, max_val = 10} : !torch.int
+    %1 = torch.symbolic_int "s1" {min_val = 2, max_val = 20} : !torch.int
+    ```
+  }];
+  let arguments = (ins
+    StrAttr:$symbol_name,
+    I64Attr:$min_val,
+    I64Attr:$max_val
+  );
+  let results = (outs
+    Torch_IntType:$result
+  );
+  let assemblyFormat = [{
+    $symbol_name ` ` `{` `min_val` `=` $min_val `,` `max_val` `=` $max_val `}` attr-dict `:` type($result)
+  }];
+}
+
+def Torch_BindSymbolicShapeOp : Torch_Op<"bind_symbolic_shape", []> {
+  let summary = "Binds shape expressions to tensors using an affine map indexed by shape symbols";
+  let description = [{
+    The `torch.bind_symbolic_shape` operation binds shape expressions
+    useful to compute the dynamic dimensions of a tensor. It takes a
+    variadic of SSA symbols that map 1:1 to the local symbols declared
+    in the affine map. The affine map contains a list of affine shape
+    expressions for each dim where the terminals are from the declared
+    symbols.
+
+    Example:
+    ```
+    torch.bind_symbolic_shape %arg0, [%0, %1], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+    torch.bind_symbolic_shape %out0, [%0, %1, %2], affine_map<()[s0, s1, s2] -> (s0, s1 * 2 + s2, 3)> : !torch.vtensor<[?,?,3],f32>
+    ```
+  }];
+  let arguments = (ins
+    Torch_ValueTensorType:$operand,
+    Variadic<Torch_IntType>:$shape_symbols,
+    Builtin_AffineMapAttr:$shape_expressions
+  );
+  let results = (outs);
+  let hasCustomAssemblyFormat = 1;
+  let hasVerifier = 1;
+}
+
 #endif // TORCH_OPS
diff --git a/lib/Dialect/Torch/IR/TorchOps.cpp b/lib/Dialect/Torch/IR/TorchOps.cpp
index 5e0f0ab1e..994722f3e 100644
--- a/lib/Dialect/Torch/IR/TorchOps.cpp
+++ b/lib/Dialect/Torch/IR/TorchOps.cpp
@@ -5034,3 +5034,65 @@ LogicalResult InitializeGlobalSlotsOp::verify() {
     return emitOpError("expected number of operands to match number of slots");
   return success();
 }
+
+//===----------------------------------------------------------------------===//
+// BindSymbolicShapeOp
+//===----------------------------------------------------------------------===//
+
+//
+// torch.bind_symbolic_shape %6, [%0, %1, %2], affine_map<()[s0, s1, s2] ->
+// (s0, s1 * 2 + s2, 3)> : !torch.vtensor<[?,?,3],f32>
+//
+
+ParseResult BindSymbolicShapeOp::parse(OpAsmParser &parser,
+                                       OperationState &result) {
+  OpAsmParser::UnresolvedOperand operand;
+  SmallVector<OpAsmParser::UnresolvedOperand> shapeSymbols;
+  AffineMapAttr shapeExpressions;
+  Type operandType;
+
+  if (parser.parseOperand(operand) || parser.parseComma() ||
+      parser.parseLSquare() || parser.parseOperandList(shapeSymbols) ||
+      parser.parseRSquare() || parser.parseComma() ||
+      parser.parseAttribute(shapeExpressions, "shape_expressions",
+                            result.attributes) ||
+      parser.parseOptionalAttrDict(result.attributes) ||
+      parser.parseColonType(operandType)) {
+    return failure();
+  }
+
+  if (parser.resolveOperand(operand, operandType, result.operands) ||
+      parser.resolveOperands(shapeSymbols,
+                             parser.getBuilder().getType<Torch::IntType>(),
+                             result.operands)) {
+    return failure();
+  }
+
+  return success();
+}
+
+// Use a custom printer here to avoid the AffineMap from getting hoisted
+// when printed. This makes it so the AffineMap is printed inline with the op.
+void BindSymbolicShapeOp::print(OpAsmPrinter &p) {
+  p << " " << getOperand() << ", [";
+  llvm::interleaveComma(getShapeSymbols(), p);
+  p << "], " << "affine_map<" << getShapeExpressions().getValue() << ">";
+  p.printOptionalAttrDict((*this)->getAttrs(),
+                          /*elidedAttrs=*/{"shape_expressions"});
+  p << " : " << getOperand().getType();
+}
+
+LogicalResult BindSymbolicShapeOp::verify() {
+  if (getShapeSymbols().empty())
+    return emitOpError() << "requires non-empty shapeSymbols";
+
+  for (auto symbol : getShapeSymbols()) {
+    Operation *definingOp = symbol.getDefiningOp();
+    if (!isa<SymbolicIntOp>(definingOp)) {
+      return emitOpError()
+             << "shape symbol must be produced by a SymbolicIntOp";
+    }
+  }
+
+  return success();
+}
diff --git a/projects/pt1/python/torch_mlir_e2e_test/configs/fx_importer_backend.py b/projects/pt1/python/torch_mlir_e2e_test/configs/fx_importer_backend.py
index 4cda217a1..11a6ef6ff 100644
--- a/projects/pt1/python/torch_mlir_e2e_test/configs/fx_importer_backend.py
+++ b/projects/pt1/python/torch_mlir_e2e_test/configs/fx_importer_backend.py
@@ -49,6 +49,9 @@ class FxImporterTestConfig(TestConfig):
                 prog,
                 output_type=self._output_type,
                 func_name=artifact.__class__.__name__,
+                # While the current e2e tests don't exercise symbolic shapes,
+                # enabling this here ensures they don't regress either.
+                import_symbolic_shape_expressions=True,
             )
             module = self._backend.compile(module)
             backend_module = self._backend.load(module)
diff --git a/python/torch_mlir/extras/fx_importer.py b/python/torch_mlir/extras/fx_importer.py
index f328bc5d0..9dcb3c285 100644
--- a/python/torch_mlir/extras/fx_importer.py
+++ b/python/torch_mlir/extras/fx_importer.py
@@ -14,6 +14,8 @@ except ImportError:
 import logging
 import operator
 import re
+import sympy
+import math
 from dataclasses import dataclass
 from types import BuiltinMethodType, BuiltinFunctionType
 from typing import (
@@ -81,6 +83,14 @@ from torch.fx.node import (
 )
 
 from ..ir import (
+    AffineAddExpr,
+    AffineConstantExpr,
+    AffineExpr,
+    AffineMap,
+    AffineMapAttr,
+    AffineModExpr,
+    AffineMulExpr,
+    AffineSymbolExpr,
     Attribute,
     Block,
     Context,
@@ -258,6 +268,71 @@ else:
     SYMBOLIC_TORCH_OPS = {key for key in SYMBOLIC_OP_TO_TORCH_OP}
 
 
+@dataclass
+class RangeConstraint:
+    min_val: int
+    max_val: int
+
+
+def sympy_expr_to_semi_affine_expr(
+    expr: sympy.Expr, symbols_map: Dict[str, AffineSymbolExpr]
+) -> AffineExpr:
+    """Translate sympy expressions to MLIR (semi-)affine expressions.
+
+    Recursively traverse the sympy expr AST and build the affine expr.
+    This is not a perfect translation. Sympy expressions are much more
+    expressive and not as constrained as affine (linear) expressions are.
+    However, for the most part, we don't need to support all of sympy.
+    PyTorch only uses a subset of sympy for capturing and expressing
+    symbolic shapes, and among what's supported, we expect the semi-affine
+    expressions (https://mlir.llvm.org/docs/Dialects/Affine/#semi-affine-maps)
+    to be sufficient.
+    """
+    if isinstance(expr, sympy.Symbol):
+        return symbols_map[str(expr)]
+    elif isinstance(expr, (int, sympy.Integer)):
+        return AffineConstantExpr.get(expr)
+    # This handles both add (`s0 + c`) and subtract (`s0 - c`).
+    # The expression is `sympy.Add` in both cases but with args
+    # (s0, c) in first case and (s0, -c) in the second case.
+    elif isinstance(expr, sympy.Add):
+        affine_expr = AffineConstantExpr.get(0)
+        for arg in expr.args:
+            affine_expr = AffineAddExpr.get(
+                affine_expr, sympy_expr_to_semi_affine_expr(arg, symbols_map)
+            )
+        return affine_expr
+    elif isinstance(expr, sympy.Mul):
+        affine_expr = AffineConstantExpr.get(1)
+        for arg in expr.args:
+            affine_expr = AffineMulExpr.get(
+                affine_expr, sympy_expr_to_semi_affine_expr(arg, symbols_map)
+            )
+        return affine_expr
+    elif isinstance(expr, sympy.Pow):
+        base, exp = expr.args
+        # Only integer exponent is supported
+        # So, s1 ** s0 isn't allowed.
+        assert isinstance(exp, (int, sympy.Integer))
+        assert exp > 0, "Only positive exponents supported in sympy.Pow"
+        affine_expr = AffineConstantExpr.get(1)
+        for _ in range(exp):
+            affine_expr = AffineMulExpr.get(
+                affine_expr, sympy_expr_to_semi_affine_expr(base, symbols_map)
+            )
+        return affine_expr
+    elif isinstance(expr, sympy.Mod):
+        dividend, divisor = expr.args
+        return AffineModExpr.get(
+            sympy_expr_to_semi_affine_expr(dividend, symbols_map),
+            sympy_expr_to_semi_affine_expr(divisor, symbols_map),
+        )
+    else:
+        raise NotImplementedError(
+            f"Translation of sympy.Expr of type {type(expr)} not implemented yet."
+        )
+
+
 @dataclass(frozen=True)
 class SparsityMeta:
     """
@@ -478,6 +553,7 @@ class FxImporter:
         *,
         func_name: str = "main",
         func_visibility: Optional[str] = None,
+        import_symbolic_shape_expressions: bool = False,
     ) -> Operation:
         """Imports an ExportedProgram according to our chosen canonical representation.
 
@@ -527,6 +603,10 @@ class FxImporter:
 
         sig = prog.graph_signature
 
+        # Populate symbolic guards for dynamic shapes (if any)
+        if import_symbolic_shape_expressions:
+            self._cc.set_symbolic_guards(prog)
+
         # Invert the (producer, node_name) maps for mutated user inputs and mutated
         # buffers. This is because we hit-detect based on the input node name.
         mutated_user_inputs = {
@@ -682,7 +762,9 @@ class FxImporter:
 
         # Import all nodes and return.
         node_importer.import_nodes(
-            all_producer_nodes.values(), skip_placeholders_outputs=True
+            all_producer_nodes.values(),
+            skip_placeholders_outputs=True,
+            import_symbolic_shape_expressions=import_symbolic_shape_expressions,
         )
         node_importer.return_node_values(loc, user_outputs)
         self.symbol_table.insert(func_op)
@@ -694,6 +776,7 @@ class FxImporter:
         *,
         func_name: str = "main",
         func_visibility: Optional[str] = None,
+        import_symbolic_shape_expressions: bool = False,
     ) -> Operation:
         """Imports a consolidated torch.export.ExportedProgram instance.
 
@@ -728,6 +811,10 @@ class FxImporter:
         state_dict = prog.state_dict
         arg_replacements: Dict[str, Any] = {}
 
+        # Populate symbolic guards for dynamic shapes (if any)
+        if import_symbolic_shape_expressions:
+            self._cc.set_symbolic_guards(prog)
+
         # If there is no "constants" attribute, consult the "state_dict". Otherwise, only look
         # at "constants". Relevant upstream patch: https://github.com/pytorch/pytorch/pull/118969
         if hasattr(prog, "constants"):
@@ -774,7 +861,10 @@ class FxImporter:
                 g.erase_node(node)
 
         return self.import_stateless_graph(
-            g, func_name=func_name, func_visibility=func_visibility
+            g,
+            func_name=func_name,
+            func_visibility=func_visibility,
+            import_symbolic_shape_expressions=import_symbolic_shape_expressions,
         )
 
     def import_graph_module(self, gm: GraphModule) -> Operation:
@@ -791,6 +881,7 @@ class FxImporter:
         *,
         func_name: str = "main",
         func_visibility: Optional[str] = None,
+        import_symbolic_shape_expressions: bool = False,
     ) -> Operation:
         """Low-level import of a functionalized, assumed stateless Graph as a func.
 
@@ -815,7 +906,9 @@ class FxImporter:
             self._cc,
             entry_block,
         )
-        node_importer.import_nodes(g.nodes)
+        node_importer.import_nodes(
+            g.nodes, import_symbolic_shape_expressions=import_symbolic_shape_expressions
+        )
         self.symbol_table.insert(func)
         return func
 
@@ -870,6 +963,7 @@ class ContextCache:
         "_c",
         "_dtype_to_type",
         "_tensor_metadata_cache",
+        "_symbolic_guards",
         "_py_attr_tracker",
         # Types.
         "torch_bool_type",
@@ -888,6 +982,7 @@ class ContextCache:
         self._tensor_metadata_cache: Dict[
             Tuple[torch.Size, torch.dtype, Optional[SparsityMeta], bool], IrType
         ] = {}
+        self._symbolic_guards: Dict = {}
         self._py_attr_tracker = py_attr_tracker or RefTracker()
 
         # Common types.
@@ -1037,6 +1132,52 @@ class ContextCache:
                 return Location.file(filename, line, col=0, context=self._c)
         return Location.unknown(context=self._c)
 
+    def set_symbolic_guards(
+        self, prog: torch.export.ExportedProgram
+    ) -> Dict[str, RangeConstraint]:
+
+        def _sympy_int_to_int(val: sympy.Expr, adjust_func: Callable):
+            # Convert simple sympy Integers into concrete int
+            if val == sympy.oo:
+                return math.inf
+            if val == -sympy.oo:
+                return -math.inf
+            if isinstance(val, sympy.Integer):
+                return int(val)
+            # TODO: Remove this adjustment when fractional ranges are removed
+            return adjust_func(val)
+
+        contains_symbolic_ints = False
+        for val in prog.range_constraints.values():
+            if (
+                isinstance(val.lower, sympy.Integer)
+                and isinstance(val.upper, sympy.Integer)
+                and not val.is_bool
+            ):
+                contains_symbolic_ints = True
+                break
+        if contains_symbolic_ints:
+            # Build a map from shape symbol name to `RangeConstraint` object
+            # capturing `min_val`` and `max_val`` constraints for that
+            # symbol. Translate sympy integers to regular integers.
+            #
+            # Example:
+            #       {
+            #          's0': RangeConstraint(min_val=5, max_val=10),
+            #          's1': RangeConstraint(min_val=0, max_val=100),
+            #          's3': RangeConstraint(min_val=0, max_val=9223372036854775806),
+            #       }
+            self._symbolic_guards = {
+                str(k): RangeConstraint(
+                    _sympy_int_to_int(v.lower, math.ceil),
+                    _sympy_int_to_int(v.upper, math.floor),
+                )
+                for k, v in prog.range_constraints.items()
+            }
+
+    def get_symbolic_guards(self) -> Dict[str, RangeConstraint]:
+        return self._symbolic_guards
+
 
 class GraphNodeImporter:
     """Imports graph nodes into an MLIR function.
@@ -1050,6 +1191,7 @@ class GraphNodeImporter:
         "_cc",
         "_on_node_produced",
         "_v",
+        "_symbol_to_value",
         "_multi_result_nodes",
         "fx_importer",
     ]
@@ -1068,6 +1210,8 @@ class GraphNodeImporter:
         # Map of (Node, result_index) to MLIR Value or a callback that lazily
         # constructs and returns a value.
         self._v: Dict[Union[Callable[[], Value], Tuple[torch_fx.Node, int]], Value] = {}
+        # Map of Shape Symbol to MLIR Value
+        self._symbol_to_value: Dict[str, Value] = {}
         # Map of node name to hook that should be called when it is produced.
         self._on_node_produced: Dict[str, Callable[[Value], None]] = {}
         # Statically multi-result nodes which we have de-tupled are noted here.
@@ -1108,6 +1252,28 @@ class GraphNodeImporter:
         self._v[key] = value
         return value
 
+    def bind_symbol_value(
+        self,
+        shape_symbol: str,
+        value: Value,
+    ):
+        """Binds a shape symbol to a global SSA value (and asserts if already bound)."""
+        assert (
+            shape_symbol not in self._symbol_to_value
+        ), f"Symbol already has a value: {shape_symbol}"
+        self._symbol_to_value[shape_symbol] = value
+
+    def resolve_symbol_value(self, shape_symbol: str) -> Value:
+        """Resolves a shape symbol to a value."""
+        try:
+            binding = self._symbol_to_value[shape_symbol]
+        except KeyError:
+            raise KeyError(
+                f"Shape symbol {shape_symbol} has not been bound to an MLIR value"
+            )
+        if isinstance(binding, Value):
+            return binding
+
     def import_mutable_to_vtensor(
         self, loc: Location, node: Node, mutable_value: Value, producer_node_name: str
     ) -> Value:
@@ -1190,10 +1356,20 @@ class GraphNodeImporter:
             func_dialect.ReturnOp(operands, loc=loc)
 
     def import_nodes(
-        self, nodes: Iterable[Node], *, skip_placeholders_outputs: bool = False
+        self,
+        nodes: Iterable[Node],
+        *,
+        skip_placeholders_outputs: bool = False,
+        import_symbolic_shape_expressions: bool = False,
     ):
         with InsertionPoint(self._b):
             loc = Location.unknown()
+
+            # Import dynamic shape symbols and guards (if any)
+            if import_symbolic_shape_expressions:
+                symbolic_guards = self._cc.get_symbolic_guards()
+                self._import_shape_symbols_with_guards(loc, symbolic_guards)
+
             num_placeholders = 0
             for node in nodes:
                 op = node.op
@@ -1253,6 +1429,8 @@ class GraphNodeImporter:
                     operands = [self._import_argument(loc, arg) for arg in node.args[0]]
                     func_dialect.ReturnOp(operands, loc=loc)
 
+                self._create_bind_symbolic_shape_ops(loc, node)
+
     def _promote_symbolic_scalar_int_float(self, loc, graph, param):
         temp_target = torch.ops.aten.Float.Scalar
         temp_node = Node(
@@ -1516,6 +1694,69 @@ class GraphNodeImporter:
         for i, value in enumerate(operation.results):
             self.bind_node_value(node, value, i)
 
+    def _import_shape_symbols_with_guards(
+        self, loc: Location, symbolic_guards: Dict[str, RangeConstraint]
+    ):
+        for symbol, constraints in symbolic_guards.items():
+            # Create torch.sym_int ops
+            operation = Operation.create(
+                name="torch.symbolic_int",
+                attributes={
+                    "symbol_name": StringAttr.get(symbol),
+                    "min_val": self._cc.integer_attr(constraints.min_val, 64),
+                    "max_val": self._cc.integer_attr(constraints.max_val, 64),
+                },
+                results=[self._cc.torch_int_type],
+                loc=loc,
+            )
+            self.bind_symbol_value(symbol, operation.result)
+
+    def _create_bind_symbolic_shape_ops(self, loc: Location, node: torch_fx.Node):
+        node_val = node.meta.get("val")
+        if (node_val is not None) and isinstance(node_val, TorchFakeTensor):
+            # Only create bind ops if the shapes contain symbolic sizes.
+            # Query the bool attribute `_has_symbolic_sizes_strides` on node.meta["val"].
+            if node_val._has_symbolic_sizes_strides:
+                # Read node metadata to obtain shape symbols and expressions
+                symbols_set = set()
+                shape_exprs = []
+                for s in node_val.size():
+                    if isinstance(s, torch.SymInt):
+                        symbols_set.update(s.node.expr.free_symbols)
+                        shape_exprs.append(s.node.expr)
+                    else:
+                        assert isinstance(s, int)
+                        shape_exprs.append(s)
+
+                # Map from sympy shape symbols to local symbols in the affine map
+                symbols_set = sorted(symbols_set, key=lambda x: x.name)
+                symbols_map = {
+                    str(symbol): AffineSymbolExpr.get(i)
+                    for i, symbol in enumerate(symbols_set)
+                }
+
+                # Convert symbolic shape expressions into affine expressions
+                affine_exprs = [
+                    sympy_expr_to_semi_affine_expr(expr, symbols_map)
+                    for expr in shape_exprs
+                ]
+
+                affine_map = AffineMap.get(0, len(symbols_set), affine_exprs)
+
+                # Build operand list
+                operand_list = []
+                operand_list.append(self.resolve_node_value(node))
+                for symbol in symbols_map.keys():
+                    operand_list.append(self.resolve_symbol_value(symbol))
+
+                # Create torch.bind_symbolic_shape ops
+                Operation.create(
+                    name="torch.bind_symbolic_shape",
+                    attributes={"shape_expressions": AffineMapAttr.get(affine_map)},
+                    operands=operand_list,
+                    loc=loc,
+                )
+
     def _import_argument(
         self, loc: Location, arg: NodeArgument, expected_jit_type=None
     ) -> Value:
diff --git a/python/torch_mlir/fx.py b/python/torch_mlir/fx.py
index b8765b659..5cd7d2d6e 100644
--- a/python/torch_mlir/fx.py
+++ b/python/torch_mlir/fx.py
@@ -54,6 +54,7 @@ def export_and_import(
     fx_importer: Optional[FxImporter] = None,
     dynamic_shapes: Optional[Union[Dict[str, Any], Tuple[Any]]] = None,
     experimental_support_mutation: bool = False,
+    import_symbolic_shape_expressions: bool = False,
     hooks: Optional[FxImporterHooks] = None,
     decomposition_table: Optional[Dict[torch._ops.OperatorBase, Callable]] = None,
     func_name: str = "main",
@@ -79,9 +80,17 @@ def export_and_import(
     if experimental_support_mutation:
         if torch.__version__ < "2.3.0.dev20240207":
             warnings.warn("Mutable program import only supported on PyTorch 2.3+")
-        fx_importer.import_program(prog, func_name=func_name)
+        fx_importer.import_program(
+            prog,
+            func_name=func_name,
+            import_symbolic_shape_expressions=import_symbolic_shape_expressions,
+        )
     else:
-        fx_importer.import_frozen_program(prog, func_name=func_name)
+        fx_importer.import_frozen_program(
+            prog,
+            func_name=func_name,
+            import_symbolic_shape_expressions=import_symbolic_shape_expressions,
+        )
 
     return _module_lowering(
         enable_ir_printing, OutputType.get(output_type), fx_importer.module
diff --git a/test/Dialect/Torch/canonicalize.mlir b/test/Dialect/Torch/canonicalize.mlir
index 180b6aac5..250f11cf6 100644
--- a/test/Dialect/Torch/canonicalize.mlir
+++ b/test/Dialect/Torch/canonicalize.mlir
@@ -3026,3 +3026,35 @@ func.func @torch.aten.clone$no_fold(%arg0: !torch.vtensor<[1,2,50,4],f32>) -> (!
   %1 = torch.copy.to_tensor %0 : !torch.tensor
   return %1 : !torch.tensor
 }
+
+
+// -----
+
+// CHECK-LABEL:   @torch.symbolic_int$canonicalize(
+// CHECK-SAME:        %[[ARG0:.*]]: !torch.vtensor<[?],f32>,
+// CHECK-SAME:        %[[ARG1:.*]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+// CHECK:               %[[S0:.*]] = torch.symbolic_int "s0" {min_val = 3, max_val = 6} : !torch.int
+// CHECK-NOT:           %[[S1:.*]] = torch.symbolic_int "s0 + 1" {min_val = 4, max_val = 7} : !torch.int
+// CHECK:               torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+// CHECK:               torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0 + 1)> : !torch.vtensor<[?],f32>
+// CHECK:               %[[V1:.*]] = torch.aten.slice.Tensor %[[ARG1]], {{.*}}, {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[?],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[?],f32>
+// CHECK:               torch.bind_symbolic_shape %[[V1]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+// CHECK:               %[[V2:.*]] = torch.aten.add.Tensor %[[ARG0]], {{.*}}, {{.*}} : !torch.vtensor<[?],f32>, !torch.vtensor<[?],f32>, !torch.int -> !torch.vtensor<[?],f32>
+// CHECK:               torch.bind_symbolic_shape %[[V2]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+// CHECK:               return %[[V2]] : !torch.vtensor<[?],f32>
+func.func @torch.symbolic_int$canonicalize(%arg0: !torch.vtensor<[?],f32>, %arg1: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+  %0 = torch.symbolic_int "s0" {min_val = 3, max_val = 6} : !torch.int
+  %1 = torch.symbolic_int "s0 + 1" {min_val = 4, max_val = 7} : !torch.int
+  torch.bind_symbolic_shape %arg0, [%0], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+  torch.bind_symbolic_shape %arg1, [%0], affine_map<()[s0] -> (s0 + 1)> : !torch.vtensor<[?],f32>
+  %int0 = torch.constant.int 0
+  %int1 = torch.constant.int 1
+  %int9223372036854775807 = torch.constant.int 9223372036854775807
+  %int1_0 = torch.constant.int 1
+  %2 = torch.aten.slice.Tensor %arg1, %int0, %int1, %int9223372036854775807, %int1_0 : !torch.vtensor<[?],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[?],f32>
+  torch.bind_symbolic_shape %2, [%0], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+  %int1_1 = torch.constant.int 1
+  %3 = torch.aten.add.Tensor %arg0, %2, %int1_1 : !torch.vtensor<[?],f32>, !torch.vtensor<[?],f32>, !torch.int -> !torch.vtensor<[?],f32>
+  torch.bind_symbolic_shape %3, [%0], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+  return %3 : !torch.vtensor<[?],f32>
+}
diff --git a/test/Dialect/Torch/invalid.mlir b/test/Dialect/Torch/invalid.mlir
index 63aa1e375..5b732788f 100644
--- a/test/Dialect/Torch/invalid.mlir
+++ b/test/Dialect/Torch/invalid.mlir
@@ -375,3 +375,22 @@ func.func @foo(%arg0: !torch.vtensor<[64,64],f32,#SV>) -> !torch.vtensor<[64,64]
 
 // expected-error @+1 {{invalid sparsity encoding attribute}}
 func.func private @tensor.sparse() -> !torch.vtensor<[64,64],f32,12345>
+
+
+// -----
+
+func.func @torch.symbolic_int$no_shape_symbols(%arg0: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+  %0 = torch.symbolic_int "s0" {min_val = 3, max_val = 6} : !torch.int
+  // expected-error @+1 {{op requires non-empty shapeSymbols}}
+  torch.bind_symbolic_shape %arg0, [], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+  return %arg0 : !torch.vtensor<[?],f32>
+}
+
+// -----
+
+func.func @torch.symbolic_int$no_shape_symbols(%arg0: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+  %int0 = torch.constant.int 0
+  // expected-error @+1 {{shape symbol must be produced by a SymbolicIntOp}}
+  torch.bind_symbolic_shape %arg0, [%int0], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+  return %arg0 : !torch.vtensor<[?],f32>
+}
diff --git a/test/python/fx_importer/basic_test.py b/test/python/fx_importer/basic_test.py
index fde318630..fbc8fdff3 100644
--- a/test/python/fx_importer/basic_test.py
+++ b/test/python/fx_importer/basic_test.py
@@ -89,6 +89,11 @@ def test_import_frozen_exported_program_with_func_name():
 @run
 # CHECK-LABEL: test_import_frozen_exported_program_with_dynamic_shapes
 # CHECK:     func.func @test_net(%[[ARG0:[a-zA-Z0-9]+]]: !torch.vtensor<[?,4],f32>) -> !torch.vtensor<[?,4],f32>
+# CHECK:     %[[S0:.*]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:     torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0, 4)> : !torch.vtensor<[?,4],f32>
+# CHECK:     %[[TANH:.*]] = torch.aten.tanh %[[ARG0]] : !torch.vtensor<[?,4],f32> -> !torch.vtensor<[?,4],f32>
+# CHECK:     torch.bind_symbolic_shape %[[TANH]], [%[[S0]]], affine_map<()[s0] -> (s0, 4)> : !torch.vtensor<[?,4],f32>
+# CHECK:     return %[[TANH]] : !torch.vtensor<[?,4],f32>
 def test_import_frozen_exported_program_with_dynamic_shapes():
     class Basic(nn.Module):
         def __init__(self):
@@ -100,7 +105,11 @@ def test_import_frozen_exported_program_with_dynamic_shapes():
     batch = Dim("batch")
     dynamic_shapes = {"x": {0: batch}}
     m = fx.export_and_import(
-        Basic(), torch.randn(3, 4), dynamic_shapes=dynamic_shapes, func_name="test_net"
+        Basic(),
+        torch.randn(3, 4),
+        dynamic_shapes=dynamic_shapes,
+        func_name="test_net",
+        import_symbolic_shape_expressions=True,
     )
     print(m)
 
@@ -108,6 +117,12 @@ def test_import_frozen_exported_program_with_dynamic_shapes():
 @run
 # CHECK-LABEL: test_broadcast_with_dynamic_shapes
 # CHECK:     func.func @test_net(%[[ARG0:[a-zA-Z0-9]+]]: !torch.vtensor<[1,2],f32>, %[[ARG1:[a-zA-Z0-9]+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?,2],f32>
+# CHECK:     %[[S0:.*]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:     torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:     torch.aten.size.int
+# CHECK:     torch.prim.ListConstruct
+# CHECK:     %[[EXPAND:.*]] = torch.aten.expand
+# CHECK:     torch.bind_symbolic_shape %[[EXPAND]], [%[[S0]]], affine_map<()[s0] -> (s0, 2)> : !torch.vtensor<[?,2],f32>
 def test_broadcast_with_dynamic_shapes():
     class Basic(nn.Module):
         def __init__(self):
@@ -127,7 +142,12 @@ def test_broadcast_with_dynamic_shapes():
     }
 
     m = fx.export_and_import(
-        Basic(), x, y, dynamic_shapes=dynamic_shapes, func_name="test_net"
+        Basic(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        func_name="test_net",
+        import_symbolic_shape_expressions=True,
     )
     print(m)
 
diff --git a/test/python/fx_importer/symbolic_shape_expr_test.py b/test/python/fx_importer/symbolic_shape_expr_test.py
new file mode 100644
index 000000000..3215e0f82
--- /dev/null
+++ b/test/python/fx_importer/symbolic_shape_expr_test.py
@@ -0,0 +1,463 @@
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+# Also available under a BSD-style license. See LICENSE.
+
+# RUN: %PYTHON %s | FileCheck %s
+# This file contains tests of various op special forms that the fx_importer
+# handles.
+
+import torch
+import torch.export
+import torch.nn as nn
+from torch.export import Dim
+
+from torch_mlir import fx
+
+
+def run(f):
+    print(f"{f.__name__}")
+    print("-" * len(f.__name__))
+    f()
+    print()
+
+
+@run
+# CHECK-LABEL: test_tanh_sigmoid_cat
+# CHECK:      func.func @main(
+# CHECK-SAME:       %[[ARG0:[a-zA-Z0-9]+]]: !torch.vtensor<[?,?,3],f32>,
+# CHECK-SAME:       %[[ARG1:[a-zA-Z0-9]+]]: !torch.vtensor<[?,?,3],f32>,
+# CHECK-SAME:       %[[ARG2:[a-zA-Z0-9]+]]: !torch.vtensor<[?,?,3],f32>) -> !torch.vtensor<[?,?,3],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = 5, max_val = 10} : !torch.int
+# CHECK:        %[[S1:.+]] = torch.symbolic_int "s1" {min_val = {{[0-9]+}}, max_val = 100} : !torch.int
+# CHECK:        %[[S2:.+]] = torch.symbolic_int "s3" {min_val = {{[0-9]+}}, max_val = 50} : !torch.int
+# CHECK:        %[[S3:.+]] = torch.symbolic_int "s5" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]], %[[S1]]], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S0]], %[[S2]]], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[ARG2]], [%[[S0]], %[[S3]]], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        %[[TANH:.+]] = torch.aten.tanh %[[ARG0]] : !torch.vtensor<[?,?,3],f32> -> !torch.vtensor<[?,?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[TANH]], [%[[S0]], %[[S1]]], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        %[[SIG:.+]] = torch.aten.sigmoid %[[ARG1]] : !torch.vtensor<[?,?,3],f32> -> !torch.vtensor<[?,?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[SIG]], [%[[S0]], %[[S2]]], affine_map<()[s0, s1] -> (s0, s1, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        %[[LIST:.+]] = torch.prim.ListConstruct %[[TANH]], %[[TANH]], %[[SIG]], %[[ARG2]] : (!torch.vtensor<[?,?,3],f32>, !torch.vtensor<[?,?,3],f32>, !torch.vtensor<[?,?,3],f32>, !torch.vtensor<[?,?,3],f32>) -> !torch.list<vtensor>
+# CHECK:        %[[CAT:.+]] = torch.aten.cat %[[LIST]], {{.*}} : !torch.list<vtensor>, !torch.int -> !torch.vtensor<[?,?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[CAT]], [%[[S0]], %[[S1]], %[[S2]], %[[S3]]], affine_map<()[s0, s1, s2, s3] -> (s0, s2 + s3 + s1 * 2, 3)> : !torch.vtensor<[?,?,3],f32>
+# CHECK:        return %[[CAT]] : !torch.vtensor<[?,?,3],f32>
+def test_tanh_sigmoid_cat():
+    class TanhSigmoidCat(nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x, y, z):
+            a = torch.tanh(x)
+            b = torch.sigmoid(y)
+            return torch.cat((a, a, b, z), dim=1)
+
+    # Sample inputs
+    x = torch.randn(5, 2, 3)
+    y = torch.randn(5, 6, 3)
+    z = torch.randn(5, 4, 3)
+
+    # Dynamic dim constraints
+    dim_n = Dim("n", min=5, max=10)
+    dim_x1 = Dim("x1", max=100)
+    dim_y1 = Dim("y1", max=50)
+    dim_z1 = Dim("z1")
+    dynamic_shapes = {
+        "x": {0: dim_n, 1: dim_x1},
+        "y": {0: dim_n, 1: dim_y1},
+        "z": {0: dim_n, 1: dim_z1},
+    }
+
+    m = fx.export_and_import(
+        TanhSigmoidCat(),
+        x,
+        y,
+        z,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_symbolic_dim_differ_by_one
+# CHECK:      func.func @main(%[[ARG0:[a-zA-Z0-9]+]]: !torch.vtensor<[?],f32>, %[[ARG1:[a-zA-Z0-9]+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> attributes {torch.assume_strict_symbolic_shapes} {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = 3, max_val = 6} : !torch.int
+# This appears in torch-nightly, but not in torch-stable (re-enable once we've moved torch-stable to 2.4+)
+# CHECK-DISABLED:   %[[S1:.+]] = torch.symbolic_int "s0 + 1" {min_val = 4, max_val = 7} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0 + 1)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[SLICE:.+]] = torch.aten.slice.Tensor %arg1, {{.*}}, {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[?],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[SLICE]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[ADD:.+]] = torch.aten.add.Tensor %[[ARG0]], %[[SLICE]], {{.*}} : !torch.vtensor<[?],f32>, !torch.vtensor<[?],f32>, !torch.int -> !torch.vtensor<[?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[ADD]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        return %[[ADD]] : !torch.vtensor<[?],f32>
+def test_symbolic_dim_differ_by_one():
+    class SymbolicDimDifferByOne(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x, y):
+            return x + y[1:]
+
+    # Sample inputs
+    x = torch.randn(5)
+    y = torch.randn(6)
+
+    # Dynamic dim constraints
+    dimx = Dim("dimx", min=3, max=6)
+    dimy = dimx + 1
+    dynamic_shapes = {
+        "x": {0: dimx},
+        "y": {0: dimy},
+    }
+
+    m = fx.export_and_import(
+        SymbolicDimDifferByOne(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        experimental_support_mutation=True,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_outer_with_squared_shape
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[VIEW1:.+]] = torch.aten.view %[[ARG0]], {{.*}} : !torch.vtensor<[?],f32>, !torch.list<int> -> !torch.vtensor<[?,1],f32>
+# CHECK:        torch.bind_symbolic_shape %[[VIEW1]], [%[[S0]]], affine_map<()[s0] -> (s0, 1)> : !torch.vtensor<[?,1],f32>
+# CHECK:        %[[MUL:.+]] = torch.aten.mul.Tensor %[[VIEW1]], %[[ARG0]] : !torch.vtensor<[?,1],f32>, !torch.vtensor<[?],f32> -> !torch.vtensor<[?,?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[MUL]], [%[[S0]]], affine_map<()[s0] -> (s0, s0)> : !torch.vtensor<[?,?],f32>
+# CHECK:        %[[VIEW2:.+]] = torch.aten.view %[[MUL]], {{.*}} : !torch.vtensor<[?,?],f32>, !torch.list<int> -> !torch.vtensor<[?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[VIEW2]], [%[[S0]]], affine_map<()[s0] -> (s0 * s0)> : !torch.vtensor<[?],f32>
+# CHECK:        return %[[VIEW2]] : !torch.vtensor<[?],f32>
+def test_outer_with_squared_shape():
+    class OuterWithSquaredShape(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor) -> torch.Tensor:
+            return torch.outer(x, x).flatten()
+
+    # Sample inputs
+    x = torch.rand(10)
+
+    # Dynamic dim constraints
+    batch = Dim("batch")
+    dynamic_shapes = {"x": {0: batch}}
+
+    m = fx.export_and_import(
+        OuterWithSquaredShape(),
+        x,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_slice_tensor_static_output
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[?,3],f32>) -> !torch.vtensor<[2,1],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = 3, max_val = 9223372036854775806} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0, 3)> : !torch.vtensor<[?,3],f32>
+# CHECK:        %[[SLICE1:.+]] = torch.aten.slice.Tensor %[[ARG0]], {{.*}}, {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[?,3],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[2,3],f32>
+# CHECK:        %[[SLICE2:.+]] = torch.aten.slice.Tensor %[[SLICE1]], {{.*}}, {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[2,3],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[2,1],f32>
+# CHECK:        return %[[SLICE2]] : !torch.vtensor<[2,1],f32>
+def test_slice_tensor_static_output():
+    class SliceTensorStaticOutput(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor) -> torch.Tensor:
+            return x[0:2, :1]
+
+    # Sample inputs
+    x = torch.randn(4, 3)
+
+    # Dynamic dim constraints
+    batch = Dim("batch", min=3)
+    dynamic_shapes = {"x": {0: batch}}
+
+    m = fx.export_and_import(
+        SliceTensorStaticOutput(),
+        x,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_slice_tensor_dynamic_output
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = 5, max_val = 9223372036854775806} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[SLICE:.+]] = torch.aten.slice.Tensor %[[ARG0]], {{.*}}, {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[?],f32>, !torch.int, !torch.int, !torch.int, !torch.int -> !torch.vtensor<[?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[SLICE]], [%[[S0]]], affine_map<()[s0] -> (s0 - 5)> : !torch.vtensor<[?],f32>
+# CHECK:        return %[[SLICE]] : !torch.vtensor<[?],f32>
+def test_slice_tensor_dynamic_output():
+    class SliceTensorDynamicOutput(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x):
+            return x[5:]
+
+    # Sample inputs
+    x = torch.randn(10)
+
+    # Dynamic dim constraints
+    dimx = Dim("dimx", min=5)
+    dynamic_shapes = {"x": {0: dimx}}
+
+    m = fx.export_and_import(
+        SliceTensorDynamicOutput(),
+        x,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_div_tensor_mixed_ranks
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[],f32>, %[[ARG1:.+]]: !torch.vtensor<[?,3],f32>) -> !torch.vtensor<[?,3],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0, 3)> : !torch.vtensor<[?,3],f32>
+# CHECK:        %[[DIV:.+]] = torch.aten.div.Tensor %[[ARG0]], %[[ARG1]] : !torch.vtensor<[],f32>, !torch.vtensor<[?,3],f32> -> !torch.vtensor<[?,3],f32>
+# CHECK:        torch.bind_symbolic_shape %[[DIV]], [%[[S0]]], affine_map<()[s0] -> (s0, 3)> : !torch.vtensor<[?,3],f32>
+# CHECK:        return %[[DIV]] : !torch.vtensor<[?,3],f32>
+def test_div_tensor_mixed_ranks():
+    class DivTensorMixedRanks(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
+            div = torch.div(x, y)
+            return div
+
+    # Sample inputs
+    x = torch.tensor(10.0)
+    y = torch.randn(2, 3)
+
+    # Dynamic dim constraints
+    batch = Dim("batch")
+    dynamic_shapes = {"x": None, "y": {0: batch}}
+
+    m = fx.export_and_import(
+        DivTensorMixedRanks(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_shape_div
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[?,7],f32>) -> !torch.vtensor<[?,5],f32> {
+# This appears in torch-nightly, but not in torch-stable (re-enable once we've moved torch-stable to 2.4+)
+# CHECK-DISABLED:        %[[S0:.+]] = torch.symbolic_int "5*s1" {min_val = 0, max_val = 5000} : !torch.int
+# CHECK:        %[[S1:.+]] = torch.symbolic_int "s1" {min_val = 2, max_val = 1000} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S1]]], affine_map<()[s0] -> (s0 * 5, 7)> : !torch.vtensor<[?,7],f32>
+# CHECK:        %[[VIEW:.+]] = torch.aten.view %[[ARG0]], {{.*}} : !torch.vtensor<[?,7],f32>, !torch.list<int> -> !torch.vtensor<[?,5],f32>
+# CHECK:        torch.bind_symbolic_shape %[[VIEW]], [%[[S1]]], affine_map<()[s0] -> (s0 * 7, 5)> : !torch.vtensor<[?,5],f32>
+# CHECK:        return %[[VIEW]] : !torch.vtensor<[?,5],f32>
+def test_shape_div():
+    class ShapeDiv(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor) -> torch.Tensor:
+            return x.reshape(-1, 5)
+
+    # Sample inputs
+    x = torch.rand(10, 7)
+
+    # Dynamic dim constraints
+    batch = Dim("batch", max=1000) * 5
+    dynamic_shapes = {"x": {0: batch}}
+
+    m = fx.export_and_import(
+        ShapeDiv(),
+        x,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_broadcast_unit_dim_to_static_with_unchanged_dim_dynamic
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[1,?],f32>) -> !torch.vtensor<[3,?],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (1, s0)> : !torch.vtensor<[1,?],f32>
+# CHECK:        %[[EXPAND:.+]] = torch.aten.expand %[[ARG0]], {{.*}}, {{.*}} : !torch.vtensor<[1,?],f32>, !torch.list<int>, !torch.bool -> !torch.vtensor<[3,?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[EXPAND]], [%[[S0]]], affine_map<()[s0] -> (3, s0)> : !torch.vtensor<[3,?],f32>
+# CHECK:        return %[[EXPAND]] : !torch.vtensor<[3,?],f32>
+def test_broadcast_unit_dim_to_static_with_unchanged_dim_dynamic():
+    class BroadcastUnitDimToStaticWithUnchangedDimDynamic(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor) -> torch.Tensor:
+            return torch.broadcast_to(x, (3, -1))
+
+    # Sample inputs
+    x = torch.randn(1, 2)
+
+    # Dynamic dim constraints
+    dim_1 = Dim("dim_1")
+    dynamic_shapes = {"x": {1: dim_1}}
+
+    m = fx.export_and_import(
+        BroadcastUnitDimToStaticWithUnchangedDimDynamic(),
+        x,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_broadcast_unit_dim_to_dynamic_with_unchanged_dim_static
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[1,2],f32>, %[[ARG1:.+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?,2],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[EXPAND:.+]] = torch.aten.expand %[[ARG0]], {{.*}}, {{.*}} : !torch.vtensor<[1,2],f32>, !torch.list<int>, !torch.bool -> !torch.vtensor<[?,2],f32>
+# CHECK:        torch.bind_symbolic_shape %[[EXPAND]], [%[[S0]]], affine_map<()[s0] -> (s0, 2)> : !torch.vtensor<[?,2],f32>
+# CHECK:        return %3 : !torch.vtensor<[?,2],f32>
+def test_broadcast_unit_dim_to_dynamic_with_unchanged_dim_static():
+    class BroadcastUnitDimToDynamicWithUnchangedDimStatic(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
+            return torch.broadcast_to(x, (y.shape[0], -1))
+
+    # Sample inputs
+    x = torch.randn(1, 2)
+    y = torch.randn(10)
+
+    # Dynamic dim constraints
+    dim_0 = Dim("dim_0")
+    dynamic_shapes = {"x": {}, "y": {0: dim_0}}
+
+    m = fx.export_and_import(
+        BroadcastUnitDimToDynamicWithUnchangedDimStatic(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_broadcast_unit_dim_to_dynamic_with_unchanged_dim_dynamic
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[1,?],f32>, %[[ARG1:.+]]: !torch.vtensor<[?],f32>) -> !torch.vtensor<[?,?],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        %[[S1:.+]] = torch.symbolic_int "s1" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (1, s0)> : !torch.vtensor<[1,?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S1]]], affine_map<()[s0] -> (s0)> : !torch.vtensor<[?],f32>
+# CHECK:        %[[EXPAND:.+]] = torch.aten.expand %[[ARG0]], {{.*}}, {{.*}} : !torch.vtensor<[1,?],f32>, !torch.list<int>, !torch.bool -> !torch.vtensor<[?,?],f32>
+# CHECK:        torch.bind_symbolic_shape %[[EXPAND]], [%[[S0]], %[[S1]]], affine_map<()[s0, s1] -> (s1, s0)> : !torch.vtensor<[?,?],f32>
+# CHECK:        return %[[EXPAND]] : !torch.vtensor<[?,?],f32>
+def test_broadcast_unit_dim_to_dynamic_with_unchanged_dim_dynamic():
+    class BroadcastUnitDimToDynamicWithUnchangedDimDynamic(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
+            return torch.broadcast_to(x, (y.shape[0], -1))
+
+    # Sample inputs
+    x = torch.randn(1, 2)
+    y = torch.randn(10)
+
+    # Dynamic dim constraints
+    dim_0 = Dim("dim_0")
+    dim_1 = Dim("dim_1")
+    dynamic_shapes = {"x": {1: dim_1}, "y": {0: dim_0}}
+
+    m = fx.export_and_import(
+        BroadcastUnitDimToDynamicWithUnchangedDimDynamic(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_broadcast_unit_dim_to_dynamic_with_rank_increase
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[1,2],f32>, %[[ARG1:.+]]: !torch.vtensor<[?,3,2],f32>) -> !torch.vtensor<[?,3,2],f32> {
+# CHECK:        %[[S0:.+]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG1]], [%[[S0]]], affine_map<()[s0] -> (s0, 3, 2)> : !torch.vtensor<[?,3,2],f32>
+# CHECK:        %[[EXPAND:.+]] = torch.aten.expand %[[ARG0]], {{.*}}, {{.*}} : !torch.vtensor<[1,2],f32>, !torch.list<int>, !torch.bool -> !torch.vtensor<[?,3,2],f32>
+# CHECK:        torch.bind_symbolic_shape %[[EXPAND]], [%[[S0]]], affine_map<()[s0] -> (s0, 3, 2)> : !torch.vtensor<[?,3,2],f32>
+# CHECK:        return %[[EXPAND]] : !torch.vtensor<[?,3,2],f32>
+def test_broadcast_unit_dim_to_dynamic_with_rank_increase():
+    class BroadcastUnitDimToDynamicWithRankIncrease(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
+            return torch.broadcast_to(x, y.size())
+
+    # Sample inputs
+    x = torch.randn(1, 2)
+    y = torch.randn(4, 3, 2)
+
+    # Dynamic dim constraints
+    dim_0 = Dim("dim_0")
+    dynamic_shapes = {"x": {}, "y": {0: dim_0}}
+
+    m = fx.export_and_import(
+        BroadcastUnitDimToDynamicWithRankIncrease(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
+
+
+@run
+# CHECK-LABEL: test_gather_elements
+# CHECK:      func.func @main(%[[ARG0:.+]]: !torch.vtensor<[?,3],f32>, %[[ARG1:.+]]: !torch.vtensor<[2,3],si64>) -> !torch.vtensor<[2,3],f32> {
+# CHECK:        %[[S0]] = torch.symbolic_int "s0" {min_val = 3, max_val = 9223372036854775806} : !torch.int
+# CHECK:        torch.bind_symbolic_shape %[[ARG0]], [%[[S0]]], affine_map<()[s0] -> (s0, 3)> : !torch.vtensor<[?,3],f32>
+# CHECK:        %[[GATHER:.+]] = torch.aten.gather %[[ARG0]], {{.*}}, {{.*}}, {{.*}} : !torch.vtensor<[?,3],f32>, !torch.int, !torch.vtensor<[2,3],si64>, !torch.bool -> !torch.vtensor<[2,3],f32>
+# CHECK:        return %[[GATHER]] : !torch.vtensor<[2,3],f32>
+def test_gather_elements():
+    class GatherElements(torch.nn.Module):
+        def __init__(self):
+            super().__init__()
+
+        def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
+            return torch.gather(x, 0, y)
+
+    # Sample inputs
+    x = torch.randn(4, 3)
+    y = torch.tensor([[0, 0, 0], [1, 1, 1]])
+
+    # Dynamic dim constraints
+    batch = Dim("batch", min=3)
+    dynamic_shapes = {"x": {0: batch}, "y": {}}
+
+    m = fx.export_and_import(
+        GatherElements(),
+        x,
+        y,
+        dynamic_shapes=dynamic_shapes,
+        import_symbolic_shape_expressions=True,
+    )
+    print(m)
diff --git a/test/python/fx_importer/sympy_to_affine_expr_test.py b/test/python/fx_importer/sympy_to_affine_expr_test.py
new file mode 100644
index 000000000..0c366040d
--- /dev/null
+++ b/test/python/fx_importer/sympy_to_affine_expr_test.py
@@ -0,0 +1,69 @@
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+# Also available under a BSD-style license. See LICENSE.
+
+# RUN: %PYTHON %s | FileCheck %s
+# This file contains tests checking translating sympy expressions to (semi-)affine expressions.
+
+from sympy import Symbol
+from torch_mlir.extras.fx_importer import sympy_expr_to_semi_affine_expr
+
+from torch_mlir.ir import (
+    AffineSymbolExpr,
+    Context,
+)
+
+
+def run(f):
+    print(f"{f.__name__}")
+    print("-" * len(f.__name__))
+    f()
+    print()
+
+
+@run
+# CHECK-LABEL: test_sympy_to_semi_affine_expr_translation
+def test_sympy_to_semi_affine_expr_translation():
+    with Context():
+        s0 = Symbol("s0", positive=True, integer=True)
+        s1 = Symbol("s1", positive=True, integer=True)
+
+        symbols_set = sorted({s0, s1}, key=lambda x: x.name)
+        symbols_map = {
+            str(symbol): AffineSymbolExpr.get(i) for i, symbol in enumerate(symbols_set)
+        }
+
+        SYMPY_EXPRS = [
+            # CHECK: 10
+            (10),
+            # CHECK: s0
+            (s0),
+            # CHECK: s0
+            (s0 + 0),
+            # CHECK: s0 + 1
+            (s0 + 1),
+            # CHECK: s0
+            (s0 * 1),
+            # CHECK: s0 * 2
+            (s0 * 2),
+            # CHECK: s0 * s0
+            (s0 * s0),
+            # CHECK: s0 * s1
+            (s0 * s1),
+            # CHECK: s0 * s0
+            (s0**2),
+            # CHECK: (s0 * s0) * s0
+            (s0**3),
+            # CHECK: ((((s0 * s0) * s0) * s0) * s0) * s0
+            ((s0**2) ** 3),
+            # CHECK: ((((((s0 * s0) * s0) * s0) * s0) * s0) * s0) * s0
+            (s0 ** (2**3)),
+            # CHECK: s0 mod 10
+            (s0 % 10),
+            # CHECK: s0 - s1 * 2 + 5
+            (s0 + 5 - 2 * s1),
+        ]
+
+        for expr in SYMPY_EXPRS:
+            print(sympy_expr_to_semi_affine_expr(expr, symbols_map))
diff --git a/test/python/fx_importer/v2.3/types_test.py b/test/python/fx_importer/v2.3/types_test.py
index 19dee8b7b..eccea125c 100644
--- a/test/python/fx_importer/v2.3/types_test.py
+++ b/test/python/fx_importer/v2.3/types_test.py
@@ -36,8 +36,13 @@ def test_scalar_typed_node():
             x = x + 1.0
             return x.shape[0]
 
+    # CHECK: %[[S0:.*]] = torch.symbolic_int "s0" {min_val = {{[0-9]+}}, max_val = {{[0-9]+}}} : !torch.int
+    # CHECK: torch.bind_symbolic_shape %arg0, [%[[S0]]], affine_map<()[s0] -> (s0, 4)> : !torch.vtensor<[?,4],f32>
     # CHECK: torch.aten.size.int %arg0, %int0 : !torch.vtensor<[?,4],f32>, !torch.int -> !torch.int
     m = fx.export_and_import(
-        Basic(), torch.randn(3, 4), dynamic_shapes={"x": {0: torch.export.Dim("b")}}
+        Basic(),
+        torch.randn(3, 4),
+        dynamic_shapes={"x": {0: torch.export.Dim("b")}},
+        import_symbolic_shape_expressions=True,
     )
     print(m)