diff --git a/lib/Conversion/TorchToLinalg/Linear.cpp b/lib/Conversion/TorchToLinalg/Linear.cpp
index b263786c3..7c5f2c88c 100644
--- a/lib/Conversion/TorchToLinalg/Linear.cpp
+++ b/lib/Conversion/TorchToLinalg/Linear.cpp
@@ -191,8 +191,9 @@ public:
     Value lhs = adaptor.getSelf();
     Value rhs = adaptor.getOther();
 
-    if (failed(verifyLinalgCompatibleTypes(op, rewriter)))
+    if (failed(verifyLinalgCompatibleTypes(op, rewriter))) {
       return failure();
+    }
     auto lhsType = lhs.getType().cast<RankedTensorType>();
     auto rhsType = rhs.getType().cast<RankedTensorType>();
 
@@ -260,7 +261,26 @@ public:
       return success();
     }
 
-    // Fourth Case: Batch-Matrix Multiplication.
+    // Fourth Case: Vec-Vec Multiplication.
+    if (lhsRank == 2 && rhsRank == 2) {
+      Value lhsDim0 = getDimOp(rewriter, loc, lhs, 0);
+      Value lhsDim1 = getDimOp(rewriter, loc, lhs, 1);
+      Value rhsDim0 = getDimOp(rewriter, loc, rhs, 0);
+      Value rhsDim1 = getDimOp(rewriter, loc, rhs, 1);
+      checkDimEqualHelper(rewriter, loc, lhsDim1, rhsDim0);
+
+      Value zeroTensor = createZeroInitTensor(
+          rewriter, loc, ValueRange{lhsDim0, rhsDim1}, elementType);
+      Value matmul =
+          rewriter
+              .create<linalg::MatmulOp>(loc, zeroTensor.getType(),
+                                        ValueRange{lhs, rhs}, zeroTensor)
+              .getResult(0);
+      rewriter.replaceOpWithNewOp<tensor::CastOp>(op, newResultType, matmul);
+      return success();
+    }
+
+    // Fifth Case: Batch-Matrix Multiplication.
     // TODO: Handle batch matrix multiplication when one of the matrix is unity
     // rank and the other has batch dimension.
     if (lhsRank > 1 && rhsRank > 1) {
diff --git a/test/Conversion/TorchToLinalg/basic.mlir b/test/Conversion/TorchToLinalg/basic.mlir
index 0aaca941b..486b8b641 100644
--- a/test/Conversion/TorchToLinalg/basic.mlir
+++ b/test/Conversion/TorchToLinalg/basic.mlir
@@ -29,6 +29,20 @@ func.func @torch.aten.mm$basic(%arg0: !torch.vtensor<[?,?],f32>, %arg1: !torch.v
 
 // -----
 
+// CHECK-LABEL: func.func @torch.aten.matmul.2d
+func.func @torch.aten.matmul.2d(%arg0: !torch.vtensor<[8,16],f32>, %arg1: !torch.vtensor<[16,8],f32>) -> !torch.vtensor<[8,8],f32> attributes {torch.onnx_meta.ir_version = 7 : si64, torch.onnx_meta.opset_version = 13 : si64, torch.onnx_meta.producer_name = "backend-test", torch.onnx_meta.producer_version = ""} {
+  // CHECK-DAG:  %[[LHS:.+]] = torch_c.to_builtin_tensor %arg0 : !torch.vtensor<[8,16],f32> -> tensor<8x16xf32>
+  // CHECK-DAG:  %[[RHS:.+]] = torch_c.to_builtin_tensor %arg1 : !torch.vtensor<[16,8],f32> -> tensor<16x8xf32>
+  // CHECK-DAG:  %[[ZERO:.+]] = arith.constant 0.000000e+00 : f32
+  // CHECK-DAG:  %[[EMPTY:.+]] = tensor.empty() : tensor<8x8xf32>
+  // CHECK-DAG:  %[[FILL:.+]] = linalg.fill ins(%[[ZERO]] : f32) outs(%[[EMPTY]] : tensor<8x8xf32>) -> tensor<8x8xf32>
+  // CHECK:  %[[MATMUL:.+]] = linalg.matmul ins(%[[LHS]], %[[RHS]] : tensor<8x16xf32>, tensor<16x8xf32>) outs(%[[FILL]] : tensor<8x8xf32>) -> tensor<8x8xf32>
+  %0 = torch.aten.matmul %arg0, %arg1 : !torch.vtensor<[8,16],f32>, !torch.vtensor<[16,8],f32> -> !torch.vtensor<[8,8],f32>
+  return %0 : !torch.vtensor<[8,8],f32>
+}
+
+// -----
+
 // CHECK-LABEL: func.func @torch.aten.mm$basic_strict(
 // CHECK-NOT: assert
 func.func @torch.aten.mm$basic_strict(%arg0: !torch.vtensor<[?,?],f32>, %arg1: !torch.vtensor<[?,?],f32>) -> !torch.vtensor<[?,2],f32>