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
@@ -373,6 +373,7 @@
   let assemblyFormat = "$arg attr-dict";
 
   let hasFolder = 1;
+  let hasCanonicalizer = 1;
 }
 
 def Shape_YieldOp : Shape_Op<"yield",
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
@@ -479,6 +479,11 @@
   return {};
 }
 
+void SizeToIndexOp::getCanonicalizationPatterns(
+    OwningRewritePatternList &patterns, MLIRContext *context) {
+  patterns.insert<IndexToSizeToIndexCanonicalization>(context);
+}
+
 //===----------------------------------------------------------------------===//
 // YieldOp
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/Shape/IR/ShapeCanonicalization.td b/mlir/lib/Dialect/Shape/IR/ShapeCanonicalization.td
--- a/mlir/lib/Dialect/Shape/IR/ShapeCanonicalization.td
+++ b/mlir/lib/Dialect/Shape/IR/ShapeCanonicalization.td
@@ -9,6 +9,7 @@
 }]>>;
 
 // Canonicalization patterns.
+
 def CstrBroadcastableEqOps : Pat<(Shape_CstrBroadcastableOp:$op $lhs, $rhs),
   (Shape_ConstWitnessOp ConstBoolAttrTrue),
   [(EqualBinaryOperands $lhs, $rhs)]>;
@@ -16,3 +17,8 @@
 def CstrEqEqOps : Pat<(Shape_CstrEqOp:$op $shapes),
   (Shape_ConstWitnessOp ConstBoolAttrTrue),
   [(AllInputShapesEq $shapes)]>;
+
+def IndexToSizeToIndexCanonicalization : Pat<
+  (Shape_SizeToIndexOp (Shape_IndexToSizeOp $arg)),
+  (replaceWithValue $arg)>;
+
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
@@ -442,3 +442,15 @@
   "consume.witness"(%0) : (!shape.witness) -> ()
   return
 }
+
+// -----
+
+// Canonicalize redundant conversion from `index` to `size` and back.
+// CHECK-LABEL: @index_to_size_to_index
+// CHECK-SAME: (%[[IDX:.*]]: index) -> index
+func @index_to_size_to_index(%index : index) -> index {
+  // CHECK: return %[[IDX]] : index
+  %size = shape.index_to_size %index
+  %result = shape.size_to_index %size
+  return %result : index
+}