diff --git a/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php b/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
index 282a180a07..fbc89780dd 100644
--- a/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
+++ b/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
@@ -2,6 +2,7 @@
 
 namespace Drupal\Tests\system\Functional\Form;
 
+use Drupal\Core\Serialization\Yaml;
 use Drupal\Tests\BrowserTestBase;
 
 /**
@@ -121,4 +122,56 @@ public function testRequiredByThemeMessage() {
     $this->assertSession()->pageTextContains('Test Theme Depending on Modules (Theme) (Disabled)');
   }
 
+  /**
+   * Tests that incompatible modules message is shown.
+   */
+  public function testInstalledIncompatibleModule() {
+    $incompatitable_modules_message = 'There are errors with some installed modules. Visit the status report page for more information.';
+    $path = \Drupal::getContainer()->getParameter('site.path') . "/modules/changing_module";
+    mkdir($path, 0777, TRUE);
+    $file_path = "$path/changing_module.info.yml";
+    $info = [
+      'name' => 'Module that changes',
+      'type' => 'module',
+    ];
+    $compatible_info = $info + ['core_version_requirement' => '*'];
+
+    file_put_contents($file_path, Yaml::encode($compatible_info));
+    $edit = ['modules[changing_module][enable]' => 'changing_module'];
+    $this->drupalGet('admin/modules');
+    $this->drupalPostForm('admin/modules', $edit, t('Install'));
+    $this->assertText('Module Module that changes has been enabled.');
+
+    $incompatible_updates = [
+      [
+        'core_version_requirement' => '^1',
+      ],
+      [
+        'core' => '8.x',
+      ],
+    ];
+    foreach ($incompatible_updates as $incompatible_update) {
+      $incompatible_info = $info + $incompatible_update;
+      file_put_contents($file_path, Yaml::encode($incompatible_info));
+      $this->drupalGet('admin/modules');
+      $this->assertText($incompatitable_modules_message);
+
+      file_put_contents($file_path, Yaml::encode($compatible_info));
+      $this->drupalGet('admin/modules');
+      $this->assertNoText($incompatitable_modules_message);
+    }
+    // Uninstall the module and ensure that incompatible modules message is not
+    // displayed for modules that are not installed.
+    $edit = ['uninstall[changing_module]' => 'changing_module'];
+    $this->drupalPostForm('admin/modules/uninstall', $edit, t('Uninstall'));
+    $this->drupalPostForm(NULL, NULL, t('Uninstall'));
+    $this->assertText('The selected modules have been uninstalled.');
+    foreach ($incompatible_updates as $incompatible_update) {
+      $incompatible_info = $info + $incompatible_update;
+      file_put_contents($file_path, Yaml::encode($incompatible_info));
+      $this->drupalGet('admin/modules');
+      $this->assertNoText($incompatitable_modules_message);
+    }
+  }
+
 }
diff --git a/core/modules/system/tests/src/Functional/Theme/ThemeUiTest.php b/core/modules/system/tests/src/Functional/Theme/ThemeUiTest.php
index d9f2d3c1a2..aa3d851684 100644
--- a/core/modules/system/tests/src/Functional/Theme/ThemeUiTest.php
+++ b/core/modules/system/tests/src/Functional/Theme/ThemeUiTest.php
@@ -2,6 +2,7 @@
 
 namespace Drupal\Tests\system\Functional\Theme;
 
+use Drupal\Core\Serialization\Yaml;
 use Drupal\Tests\BrowserTestBase;
 
 /**
@@ -318,4 +319,59 @@ public function testInstallModuleWithIncompatibleDependencies() {
     $this->assertStringContainsString('This theme requires the listed modules to operate correctly.', $theme_container->getText());
   }
 
+  /**
+   * Tests that incompatible themes message is shown.
+   */
+  public function testInstalledIncompatibleTheme() {
+    $page = $this->getSession()->getPage();
+    $assert_session = $this->assertSession();
+    $incompatitable_themes_message = 'There are errors with some installed themes. Visit the status report page for more information.';
+    $path = \Drupal::getContainer()->getParameter('site.path') . "/themes/changing_theme";
+    mkdir($path, 0777, TRUE);
+    $file_path = "$path/changing_theme.info.yml";
+    $theme_name = 'Theme that changes';
+    $info = [
+      'name' => $theme_name,
+      'type' => 'theme',
+      'base theme' => FALSE,
+    ];
+
+    $compatible_info = $info + ['core_version_requirement' => '*'];
+
+    file_put_contents($file_path, Yaml::encode($compatible_info));
+    $this->drupalGet('admin/appearance');
+    $this->assertNoText($incompatitable_themes_message);
+    $page->clickLink("Install $theme_name theme");
+    $assert_session->addressEquals('admin/appearance');
+    $assert_session->pageTextContains("The $theme_name theme has been installed");
+
+    $incompatible_updates = [
+      [
+        'core_version_requirement' => '^1',
+      ],
+      [
+        'core' => '8.x',
+      ],
+    ];
+    foreach ($incompatible_updates as $incompatible_update) {
+      $incompatible_info = $info + $incompatible_update;
+      file_put_contents($file_path, Yaml::encode($incompatible_info));
+      $this->drupalGet('admin/appearance');
+      $this->assertText($incompatitable_themes_message);
+
+      file_put_contents($file_path, Yaml::encode($compatible_info));
+      $this->drupalGet('admin/appearance');
+      $this->assertNoText($incompatitable_themes_message);
+    }
+    // Uninstall the theme and ensure that incompatible themes message is not
+    // displayed for themes that are not installed.
+    $this->uninstallTheme($theme_name);
+    foreach ($incompatible_updates as $incompatible_update) {
+      $incompatible_info = $info + $incompatible_update;
+      file_put_contents($file_path, Yaml::encode($incompatible_info));
+      $this->drupalGet('admin/appearance');
+      $this->assertNoText($incompatitable_themes_message);
+    }
+  }
+
 }