diff -u b/address.module b/address.module
--- b/address.module
+++ b/address.module
@@ -24,7 +24,8 @@
         'locality' => [],
         'administrative_area' => [],
         'country' => [],
-        'element' => [],
+        'address' => NULL,
+        'view_mode' => '',
       ],
     ],
   ];
@@ -34,18 +35,20 @@
  * Implements hook_theme_suggestions_HOOK().
  */
 function address_theme_suggestions_address_plain(array $variables) {
-  $original = $variables['theme_hook_original'];
-  $address = $variables['element']['#address'];
-  $item = $address->getParent();
-  $entity = $item->getParent()->getValue();
-  $field = $address->getFieldDefinition();
-
   $suggestions = [];
-  $suggestions[] = $original . '__' . $field->getName();
-  $suggestions[] = $original . '__' . $entity->getEntityTypeID() . '__' . $entity->bundle();
-  $suggestions[] = $original . '__' . $entity->getEntityTypeID() . '__' . $entity->bundle() . '__' . $variables['element']['#view_mode'];
-  $suggestions[] = $original . '__' . $entity->getEntityTypeID() . '__' . $field->getName();
-  $suggestions[] = $original . '__' . $entity->getEntityTypeID() . '__' . $field->getName() . '__' . $entity->bundle();
+  $original = $variables['theme_hook_original'] . '__';
+  $field = $variables['address']->getFieldDefinition();
+  $entity_type_id = $field->getTargetEntityTypeId();
+  $bundle = $field->getTargetBundle();
+  $sanitized_view_mode = strtr($variables['view_mode'], '.', '_');
+
+  $suggestions[] = $original . $entity_type_id . '__' . $sanitized_view_mode;
+  $suggestions[] = $original . $entity_type_id . '__' . $bundle;
+  $suggestions[] = $original . $entity_type_id . '__' . $bundle . '__' . $sanitized_view_mode;
+  $suggestions[] = $original . $field->getName();
+  $suggestions[] = $original . $entity_type_id . '__' . $field->getName();
+  $suggestions[] = $original . $entity_type_id . '__' . $field->getName() . '__' . $bundle;
+
   return $suggestions;
 }
 
diff -u b/src/Plugin/Field/FieldFormatter/AddressPlainFormatter.php b/src/Plugin/Field/FieldFormatter/AddressPlainFormatter.php
--- b/src/Plugin/Field/FieldFormatter/AddressPlainFormatter.php
+++ b/src/Plugin/Field/FieldFormatter/AddressPlainFormatter.php
@@ -51,13 +51,6 @@
   protected $subdivisionRepository;
 
   /**
-   * The view mode.
-   *
-   * @var \CommerceGuys\Addressing\Subdivision\SubdivisionRepositoryInterface
-   */
-  protected $viewMode;
-
-  /**
    * Constructs an AddressPlainFormatter object.
    *
    * @param string $plugin_id
@@ -87,7 +80,6 @@
     $this->addressFormatRepository = $address_format_repository;
     $this->countryRepository = $country_repository;
     $this->subdivisionRepository = $subdivision_repository;
-    $this->viewMode = $view_mode;
   }
 
   /**
@@ -155,10 +147,8 @@
         'code' => $country_code,
         'name' => $countries[$country_code],
       ],
-      '#element' => [
-        '#address' => $address,
-        '#view_mode' => $this->viewMode,
-      ],
+      '#address' => $address,
+      '#view_mode' => $this->viewMode,
       '#cache' => [
         'contexts' => [
           'languages:' . LanguageInterface::TYPE_INTERFACE,
only in patch2:
unchanged:
--- a/templates/address-plain.html.twig
+++ b/templates/address-plain.html.twig
@@ -24,6 +24,10 @@
  *   - country: The country.
  *     - country.code: Country code.
  *     - country.name: Country name.
+ *   - address: An object that implements \Drupal\address\AddressInterface
+ *     representing the address to be rendered. Only public methods can be used.
+ *   - view_mode: View mode of the entity being rendered that this address field
+ *     is attached to. For example, "teaser" or "full".
  *
  * if a subdivision (dependent_locality, locality, administrative_area) was
  * entered, the array will always have a code. If it's a predefined subdivision,
only in patch2:
unchanged:
--- a/tests/src/Kernel/Formatter/AddressPlainFormatterTest.php
+++ b/tests/src/Kernel/Formatter/AddressPlainFormatterTest.php
@@ -12,26 +12,35 @@ use Drupal\entity_test\Entity\EntityTest;
 class AddressPlainFormatterTest extends FormatterTestBase {
 
   /**
+   * The entity with an address field to test formatting with.
+   *
+   * @var \Drupal\Core\Entity\EntityInterface
+   */
+  protected $entity;
+
+  /**
    * {@inheritdoc}
    */
   protected function setUp() {
     parent::setUp();
 
     $this->createField('address', 'address_plain');
-  }
 
-  /**
-   * Tests the rendered output.
-   */
-  public function testRender() {
-    $entity = EntityTest::create([]);
-    $entity->{$this->fieldName} = [
+    $this->entity = EntityTest::create([]);
+    $this->entity->{$this->fieldName} = [
       'country_code' => 'AD',
       'locality' => 'Canillo',
       'postal_code' => 'AD500',
       'address_line1' => 'C. Prat de la Creu, 62-64',
     ];
-    $this->renderEntityFields($entity, $this->display);
+
+  }
+
+  /**
+   * Tests the rendered output.
+   */
+  public function testRender() {
+    $this->renderEntityFields($this->entity, $this->display);
 
     // Confirm the expected elements, including the predefined locality
     // (properly escaped), country name.
@@ -46,9 +55,40 @@ class AddressPlainFormatterTest extends FormatterTestBase {
     }
 
     // Confirm that an unrecognized locality is shown unmodified.
-    $entity->{$this->fieldName}->locality = 'FAKE_LOCALITY';
-    $this->renderEntityFields($entity, $this->display);
+    $this->entity->{$this->fieldName}->locality = 'FAKE_LOCALITY';
+    $this->renderEntityFields($this->entity, $this->display);
     $this->assertRaw('FAKE_LOCALITY');
   }
 
+  /**
+   * Tests the theme hook suggestions.
+   *
+   * @see \Drupal\Tests\node\Functional\NodeTemplateSuggestionsTest
+   */
+  public function testAddressPlainThemeHookSuggestions() {
+    foreach (['full', 'my_custom_view_mode'] as $view_mode) {
+      // Simulate themeing of the address test entity.
+      $variables['theme_hook_original'] = 'address_plain';
+      $variables['view_mode'] = $view_mode;
+      $variables['address'] = $this->entity->{$this->fieldName};
+      $suggestions = \Drupal::moduleHandler()->invokeAll('theme_suggestions_address_plain', [$variables]);
+
+      $expected_suggestions = [
+        // Hook __ entity_type __ view_mode.
+        'address_plain__entity_test__' . $view_mode,
+        // Hook __ entity_type __ bundle.
+        'address_plain__entity_test__entity_test',
+        // Hook __ entity_type __ bundle __ view_mode.
+        'address_plain__entity_test__entity_test__' . $view_mode,
+        // Hook __ field_name.
+        'address_plain__' . $this->fieldName,
+        // Hook __ entity_type __ field_name.
+        'address_plain__entity_test__' . $this->fieldName,
+        // Hook __ entity_type __ field_name __ bundle.
+        'address_plain__entity_test__' . $this->fieldName . '__entity_test',
+      ];
+      $this->assertEqual($suggestions, $expected_suggestions, 'Unexpected theme suggestions for ' . $view_mode);
+    }
+  }
+
 }