diff --git a/core/modules/system/lib/Drupal/system/Form/DateFormatFormBase.php b/core/modules/system/lib/Drupal/system/Form/DateFormatFormBase.php
index 2205942..e9561e1 100644
--- a/core/modules/system/lib/Drupal/system/Form/DateFormatFormBase.php
+++ b/core/modules/system/lib/Drupal/system/Form/DateFormatFormBase.php
@@ -112,6 +112,27 @@ public static function dateTimeLookup(array $form, array $form_state) {
   }
 
   /**
+   * Callback to check if a machine name cannot be used for a new date format.
+   *
+   * @param string $machine_name
+   *   The machine name.
+   * @param array $element
+   *   The form element.
+   * @param array $form_state
+   *   The form state.
+   *
+   * @return bool
+   *   TRUE if this format already exists, or is equal to "custom" or
+   *   "fallback". FALSE otherwise.
+   */
+  public function allowedMachineName($machine_name, array $element,  array $form_state) {
+    if ($machine_name == 'custom' || $machine_name == 'fallback') {
+      return TRUE;
+    }
+    return $this->exists($machine_name, $element, $form_state);
+  }
+
+  /**
    * {@inheritdoc}
    */
   public function form(array $form, array &$form_state) {
@@ -129,7 +150,7 @@ public function form(array $form, array &$form_state) {
       '#disabled' => !$this->entity->isNew(),
       '#default_value' => $this->entity->id(),
       '#machine_name' => array(
-        'exists' => array($this, 'exists'),
+        'exists' => array($this, 'allowedMachineName'),
       ),
     );
 
diff --git a/core/modules/system/lib/Drupal/system/Tests/System/DateFormatsMachineNameTest.php b/core/modules/system/lib/Drupal/system/Tests/System/DateFormatsMachineNameTest.php
new file mode 100644
index 0000000..6338aa9
--- /dev/null
+++ b/core/modules/system/lib/Drupal/system/Tests/System/DateFormatsMachineNameTest.php
@@ -0,0 +1,85 @@
+<?php
+
+/**
+ * @file
+ * Contains \Drupal\system\Tests\System\DateFormatsMachineNameTest.
+ */
+
+namespace Drupal\system\Tests\System;
+
+use Drupal\Component\Datetime\DateTimePlus;
+use Drupal\Component\Utility\Unicode;
+use Drupal\simpletest\WebTestBase;
+
+/**
+ * Functional tests for format dates machine names.
+ */
+class DateFormatsMachineNameTest extends WebTestBase {
+
+  /**
+   * Modules to enable.
+   *
+   * @var array
+   */
+  public static $modules = array('system');
+
+  public static function getInfo() {
+    return array(
+      'name' => 'Date Formats machine names',
+      'description' => 'Test DateTime date formats machine names.',
+      'group' => 'System',
+    );
+  }
+
+  public function setUp() {
+    parent::setUp();
+    // Create a new administrator user for the test.
+    $admin = $this->drupalCreateUser(array('administer site configuration'));
+    $this->drupalLogin($admin);
+  }
+
+  /**
+   * Tests that machine names cannot be created with not allowed values.
+   */
+  public function testDateFormatsMachineNameAllowedValues() {
+    // Try to create a date format with machine name "custom".
+    $edit = array(
+      'label' => 'Custom',
+      'id' => 'custom',
+      'date_format_pattern' => 'Y-m-d',
+    );
+    $this->drupalPostForm('admin/config/regional/date-time/formats/add', $edit, t('Add format'));
+    $this->assertText('The machine-readable name is already in use. It must be unique.');
+
+    // Try to create a date format with machine name "fallback".
+    $edit = array(
+      'label' => 'Fallback',
+      'id' => 'fallback',
+      'date_format_pattern' => 'j/m/Y',
+    );
+    $this->drupalPostForm('admin/config/regional/date-time/formats/add', $edit, t('Add format'));
+    $this->assertText('The machine-readable name is already in use. It must be unique.');
+
+    // Create a date format with a machine name distinct from the previous two.
+    do {
+      $id = Unicode::strtolower($this->randomName(16));
+    } while ($id == 'custom' || $id == 'fallback');
+    $edit = array(
+      'label' => $this->randomName(16),
+      'id' => $id,
+      'date_format_pattern' => 'd/m/Y',
+    );
+    $this->drupalPostForm('admin/config/regional/date-time/formats/add', $edit, t('Add format'));
+    $this->assertText('Custom date format added.');
+
+    // Try to create a date format with same machine name as the previous one.
+    $edit = array(
+      'label' => $this->randomName(16),
+      'id' => $id,
+      'date_format_pattern' => 'd-m-Y',
+    );
+    $this->drupalPostForm('admin/config/regional/date-time/formats/add', $edit, t('Add format'));
+    $this->assertText('The machine-readable name is already in use. It must be unique.');
+  }
+
+}