diff --git a/core/modules/system/system.admin.inc b/core/modules/system/system.admin.inc
index d228917c41..4cf4dba37b 100644
--- a/core/modules/system/system.admin.inc
+++ b/core/modules/system/system.admin.inc
@@ -294,7 +294,13 @@ function template_preprocess_system_themes_page(&$variables) {
       // Make sure to provide feedback on compatibility.
       $current_theme['incompatible'] = '';
       if (!empty($theme->incompatible_core)) {
-        $current_theme['incompatible'] = t("This theme is not compatible with Drupal @core_version. Check that the .info.yml file contains the correct 'core' value.", ['@core_version' => \Drupal::CORE_COMPATIBILITY]);
+        if (isset($theme->info['core'])) {
+          $current_theme['incompatible'] = t("This theme is not compatible with Drupal @core_version. It is only compatible with Drupal versions that satisfy this constraint: @core_constraint", ['@core_version' => \Drupal::VERSION, '@core_constraint' => $theme->info['core']]);
+        }
+        else {
+          $current_theme['incompatible'] = t("This theme must declare a 'core' value in its .info.yml file.");
+        }
+
       }
       elseif (!empty($theme->incompatible_region)) {
         $current_theme['incompatible'] = t("This theme is missing a 'content' region.");
diff --git a/core/modules/update/update.module b/core/modules/update/update.module
index 1327944481..c07ad7a6cb 100644
--- a/core/modules/update/update.module
+++ b/core/modules/update/update.module
@@ -11,6 +11,7 @@
  * ability to install contributed modules and themes via an user interface.
  */
 
+use Drupal\Component\Version\DrupalSemver;
 use Drupal\Core\File\Exception\FileException;
 use Drupal\Core\Link;
 use Drupal\Core\Url;
@@ -699,7 +700,7 @@ function update_verify_update_archive($project, $archive_file, $directory) {
     $info = \Drupal::service('info_parser')->parse($file->uri);
 
     // If the module or theme is incompatible with Drupal core, set an error.
-    if (empty($info['core']) || $info['core'] != \Drupal::CORE_COMPATIBILITY) {
+    if (empty($info['core']) || !DrupalSemver::satisfies(\Drupal::VERSION, $info['core'])) {
       $incompatible[] = !empty($info['name']) ? $info['name'] : t('Unknown');
     }
     else {
@@ -717,7 +718,7 @@ function update_verify_update_archive($project, $archive_file, $directory) {
       '%archive_file contains a version of %names that is not compatible with Drupal @version.',
       '%archive_file contains versions of modules or themes that are not compatible with Drupal @version: %names',
       [
-        '@version' => \Drupal::CORE_COMPATIBILITY,
+        '@version' => \Drupal::VERSION,
         '%archive_file' => $file_system->basename($archive_file),
         '%names' => implode(', ', $incompatible),
       ]