diff --git a/stubs/Collections.phpstub b/stubs/Collections.phpstub
index 165465d..6b7ea0f 100644
--- a/stubs/Collections.phpstub
+++ b/stubs/Collections.phpstub
@@ -170,6 +170,7 @@ interface Collection extends Countable, IteratorAggregate, ArrayAccess
 interface Selectable
 {
     /**
+     * @psalm-mutation-free
      * @return Collection<TKey,TValue>
      */
     public function matching(Criteria $criteria);
diff --git a/stubs/Criteria.phpstub b/stubs/Criteria.phpstub
new file mode 100644
index 0000000..abe09ae
--- /dev/null
+++ b/stubs/Criteria.phpstub
@@ -0,0 +1,24 @@
+<?php
+
+namespace Doctrine\Common\Collections;
+
+class Criteria
+{
+    public const ASC = 'ASC';
+    public const DESC = 'DESC';
+    
+    /**
+     * @psalm-pure
+     */
+    public static function create()
+    {
+    }
+    
+    /**
+     * @psalm-external-mutation-free
+     * @param array<string, Criteria::ASC|Criteria::DESC>
+     */
+    public function orderBy(array $orderings)
+    {
+    }
+}
diff --git a/tests/acceptance/Criteria.feature b/tests/acceptance/Criteria.feature
new file mode 100644
index 0000000..91e8285
--- /dev/null
+++ b/tests/acceptance/Criteria.feature
@@ -0,0 +1,58 @@
+Feature: Criteria
+  In order to use Doctrine Criteria
+  As a Psalm user
+  I need Psalm to typecheck Criteria
+
+  Background:
+    Given I have Doctrine plugin enabled
+    And I have the following code preamble
+      """
+      <?php
+      use Doctrine\Common\Collections\Collection;
+      use Doctrine\Common\Collections\Criteria;
+      use Doctrine\Common\Collections\Selectable;
+      """
+    # Psalm enables cache when there's a composer.lock file
+    And I have empty composer.lock
+    
+    @Criteria::create
+    Scenario: Creating a Criteria in a pure context
+      Given I have the following code
+      """
+      /** @psalm-pure */
+      function foo(Selectable $collection): Collection
+      {
+          return $collection->matching(Criteria::create());
+      }
+      """
+    When I run Psalm
+    Then I see no errors
+    
+    @Criteria::orderBy
+    Scenario: Order a Criteria in a pure context
+      Given I have the following code
+      """
+      /** @psalm-pure */
+      function foo(Selectable $collection): Collection
+      {
+          return $collection->matching(Criteria::create()->orderBy(['foo' => Criteria::ASC]));
+      }
+      """
+    When I run Psalm
+    Then I see no errors
+    
+    @Criteria::orderBy
+    Scenario: Invalid sorting provided to matching
+      Given I have the following code
+      """
+      /** @psalm-pure */
+      function foo(Selectable $collection): Collection
+      {
+          return $collection->matching(Criteria::create()->orderBy(['foo' => 'bar']));
+      }
+      """
+    When I run Psalm
+    Then I see these errors
+      | Type                  | Message                                                                                   |
+      | todo | todo |
+    And I see no other errors