diff --git a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
--- a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
+++ b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
@@ -326,6 +326,7 @@
   }];
 
   let verifier = [{ return ::verify(*this); }];
+  let hasFolder = 1;
 }
 
 def Shape_NumElementsOp : Shape_Op<"num_elements", [NoSideEffect]> {
diff --git a/mlir/lib/Dialect/Shape/IR/Shape.cpp b/mlir/lib/Dialect/Shape/IR/Shape.cpp
--- a/mlir/lib/Dialect/Shape/IR/Shape.cpp
+++ b/mlir/lib/Dialect/Shape/IR/Shape.cpp
@@ -695,6 +695,18 @@
   return success();
 }
 
+OpFoldResult MulOp::fold(ArrayRef<Attribute> operands) {
+  auto lhs = operands[0].dyn_cast_or_null<IntegerAttr>();
+  if (!lhs)
+    return nullptr;
+  auto rhs = operands[1].dyn_cast_or_null<IntegerAttr>();
+  if (!rhs)
+    return nullptr;
+  APInt folded = lhs.getValue() * rhs.getValue();
+  Type indexTy = IndexType::get(getContext());
+  return IntegerAttr::get(indexTy, folded);
+}
+
 //===----------------------------------------------------------------------===//
 // ShapeOfOp
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/Dialect/Shape/canonicalize.mlir b/mlir/test/Dialect/Shape/canonicalize.mlir
--- a/mlir/test/Dialect/Shape/canonicalize.mlir
+++ b/mlir/test/Dialect/Shape/canonicalize.mlir
@@ -734,3 +734,43 @@
   %result = shape.shape_eq %a, %b : !shape.shape, !shape.shape
   return %result : i1
 }
+
+// -----
+
+// Fold `mul` for constant sizes.
+// CHECK-LABEL: @fold_mul_size
+func @fold_mul_size() -> !shape.size {
+  // CHECK: %[[RESULT:.*]] = shape.const_size 6
+  // CHECK: return %[[RESULT]] : !shape.size
+  %c2 = shape.const_size 2
+  %c3 = shape.const_size 3
+  %result = shape.mul %c2, %c3 : !shape.size, !shape.size -> !shape.size
+  return %result : !shape.size
+}
+
+// -----
+
+// Fold `mul` for constant indices.
+// CHECK-LABEL: @fold_mul_index
+func @fold_mul_index() -> index {
+  // CHECK: %[[RESULT:.*]] = constant 6 : index
+  // CHECK: return %[[RESULT]] : index
+  %c2 = constant 2 : index
+  %c3 = constant 3 : index
+  %result = shape.mul %c2, %c3 : index, index -> index
+  return %result : index
+}
+
+// -----
+
+// Fold `mul` for mixed constants.
+// CHECK-LABEL: @fold_mul_mixed
+func @fold_mul_mixed() -> !shape.size {
+  // CHECK: %[[RESULT:.*]] = shape.const_size 6
+  // CHECK: return %[[RESULT]] : !shape.size
+  %c2 = shape.const_size 2
+  %c3 = constant 3 : index
+  %result = shape.mul %c2, %c3 : !shape.size, index -> !shape.size
+  return %result : !shape.size
+}
+