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
@@ -49,7 +49,7 @@
   let verifier = [{ return verifySizeOrIndexOp(*this); }];
 }
 
-def Shape_BroadcastOp : Shape_Op<"broadcast", [Commutative]> {
+def Shape_BroadcastOp : Shape_Op<"broadcast", [Commutative, NoSideEffect]> {
   let summary = "Returns the broadcasted output shape of two or more inputs";
   let description = [{
     Returns the broadcasted shape for input shapes or extent tensors. The rest
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
@@ -132,6 +132,17 @@
 
 // -----
 
+// Dead code
+// CHECK-LABEL: @broadcast
+func @broadcast(%arg0 : !shape.shape, %arg1 : !shape.shape) {
+  // CHECK-NEXT: return
+  %0 = shape.broadcast %arg0, %arg1
+      : !shape.shape, !shape.shape -> !shape.shape
+  return
+}
+
+// -----
+
 // Basic case.
 // CHECK-LABEL: func @f
 func @f() -> !shape.shape {