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
@@ -387,13 +387,48 @@
     used to return an error to the user upon mismatch of dimensions.
 
     ```mlir
-    %c = shape.join %a, %b, error="<reason>" : !shape.shape
+    %c = shape.join %a, %b, error="<reason>" : !shape.shape, !shape.shape -> !shape.shape
     ```
   }];
 
   let arguments = (ins Shape_ShapeOrSizeType:$arg0, Shape_ShapeOrSizeType:$arg1,
                    OptionalAttr<StrAttr>:$error);
   let results = (outs Shape_ShapeOrSizeType:$result);
+
+  let assemblyFormat = [{
+    $arg0 `,` $arg1 (`,` `error` `=` $error^)? attr-dict `:`
+      type($arg0) `,` type($arg1) `->` type($result)
+  }];
+}
+
+def Shape_MaxOp : Shape_Op<"max", [Commutative, NoSideEffect]> {
+  let summary = "Elementwise maximum";
+  let description = [{
+    Computes the elementwise maximum of two shapes with equal ranks. If either
+    operand an error will be propagated to the result.
+  }];
+
+  let arguments = (ins Shape_ShapeOrSizeType:$lhs, Shape_ShapeOrSizeType:$rhs);
+  let results = (outs Shape_ShapeOrSizeType:$result);
+
+  let assemblyFormat = [{
+    $lhs `,` $rhs attr-dict `:` type($lhs) `,` type($rhs) `->` type($result)
+  }];
+}
+
+def Shape_MinOp : Shape_Op<"min", [Commutative, NoSideEffect]> {
+  let summary = "Elementwise minimum";
+  let description = [{
+    Computes the elementwise minimum of two shapes with equal ranks. If either
+    operand an error will be propagated to the result.
+  }];
+
+  let arguments = (ins Shape_ShapeOrSizeType:$lhs, Shape_ShapeOrSizeType:$rhs);
+  let results = (outs Shape_ShapeOrSizeType:$result);
+
+  let assemblyFormat = [{
+    $lhs `,` $rhs attr-dict `:` type($lhs) `,` type($rhs) `->` type($result)
+  }];
 }
 
 def Shape_MulOp : Shape_Op<"mul", [Commutative, NoSideEffect]> {
diff --git a/mlir/test/Dialect/Shape/ops.mlir b/mlir/test/Dialect/Shape/ops.mlir
--- a/mlir/test/Dialect/Shape/ops.mlir
+++ b/mlir/test/Dialect/Shape/ops.mlir
@@ -115,7 +115,7 @@
 }
 
 func @eq_on_extent_tensors(%lhs : tensor<?xindex>,
-                                      %rhs : tensor<?xindex>) {
+                           %rhs : tensor<?xindex>) {
   %w0 = shape.cstr_eq %lhs, %rhs : tensor<?xindex>, tensor<?xindex>
   return
 }
@@ -183,7 +183,6 @@
   return %rank : index
 }
 
-
 func @shape_eq_on_shapes(%a : !shape.shape, %b : !shape.shape) -> i1 {
   %result = shape.shape_eq %a, %b : !shape.shape, !shape.shape
   return %result : i1
@@ -289,3 +288,19 @@
       : !shape.shape, !shape.shape
   return %result : i1
 }
+
+func @upper_bounded_by_constant(%a: !shape.shape) -> !shape.shape {
+  %0 = shape.const_shape [4, 57, 92] : !shape.shape
+  %1 = shape.max %a, %0 : !shape.shape, !shape.shape -> !shape.shape
+  %2 = shape.join %0, %1, error="exceeded element-wise upper bound" :
+    !shape.shape, !shape.shape -> !shape.shape
+  return %2 : !shape.shape
+}
+
+func @lower_bounded_by_constant(%a: !shape.shape) -> !shape.shape {
+  %0 = shape.const_shape [4, 57, 92] : !shape.shape
+  %1 = shape.min %a, %0 : !shape.shape, !shape.shape -> !shape.shape
+  %2 = shape.join %0, %1, error="lower bound element-wise exceeded" :
+    !shape.shape, !shape.shape -> !shape.shape
+  return %2 : !shape.shape
+}