diff --git a/lib/web_ui/lib/src/engine/semantics/checkable.dart b/lib/web_ui/lib/src/engine/semantics/checkable.dart
index 9c634f6f3a8f6..cf37b2423b59c 100644
--- a/lib/web_ui/lib/src/engine/semantics/checkable.dart
+++ b/lib/web_ui/lib/src/engine/semantics/checkable.dart
@@ -56,7 +56,9 @@ class Checkable extends PrimaryRoleManager {
           PrimaryRole.checkable,
           semanticsObject,
           labelRepresentation: LeafLabelRepresentation.ariaLabel,
-        );
+        ) {
+    addTappable();
+  }
 
   final _CheckableKind _kind;
 
diff --git a/lib/web_ui/lib/src/engine/semantics/link.dart b/lib/web_ui/lib/src/engine/semantics/link.dart
index bb4346b538089..d9f93078f005f 100644
--- a/lib/web_ui/lib/src/engine/semantics/link.dart
+++ b/lib/web_ui/lib/src/engine/semantics/link.dart
@@ -11,7 +11,9 @@ class Link extends PrimaryRoleManager {
     PrimaryRole.link,
     semanticsObject,
     labelRepresentation: LeafLabelRepresentation.domText,
-  );
+  ) {
+    addTappable();
+  }
 
   @override
   DomElement createElement() {
diff --git a/lib/web_ui/lib/src/engine/semantics/semantics.dart b/lib/web_ui/lib/src/engine/semantics/semantics.dart
index 4f130bb001801..3d10056c20fa6 100644
--- a/lib/web_ui/lib/src/engine/semantics/semantics.dart
+++ b/lib/web_ui/lib/src/engine/semantics/semantics.dart
@@ -439,7 +439,6 @@ abstract class PrimaryRoleManager {
     addLiveRegion();
     addRouteName();
     addLabelAndValue(labelRepresentation: labelRepresentation);
-    addTappable();
   }
 
   /// Initializes a blank role for a [semanticsObject].
@@ -625,7 +624,17 @@ final class GenericRole extends PrimaryRoleManager {
     PrimaryRole.generic,
     semanticsObject,
     labelRepresentation: LeafLabelRepresentation.domText,
-  );
+  ) {
+    // Typically a tappable widget would have a more specific role, such as
+    // "link", "button", "checkbox", etc. However, there are situations when a
+    // tappable is not a leaf node, but contains other nodes, which can also be
+    // tappable. For example, the dismiss barrier of a pop-up menu is a tappable
+    // ancestor of the menu itself, while the menu may contain tappable
+    // children.
+    if (semanticsObject.isTappable) {
+      addTappable();
+    }
+  }
 
   @override
   void update() {
diff --git a/lib/web_ui/lib/src/engine/semantics/tappable.dart b/lib/web_ui/lib/src/engine/semantics/tappable.dart
index bbcdd216c3c4b..f99faab8f55cf 100644
--- a/lib/web_ui/lib/src/engine/semantics/tappable.dart
+++ b/lib/web_ui/lib/src/engine/semantics/tappable.dart
@@ -12,6 +12,7 @@ class Button extends PrimaryRoleManager {
     semanticsObject,
     labelRepresentation: LeafLabelRepresentation.domText,
   ) {
+    addTappable();
     setAriaRole('button');
   }
 
diff --git a/lib/web_ui/test/engine/semantics/semantics_test.dart b/lib/web_ui/test/engine/semantics/semantics_test.dart
index 661553b3be569..34dd6c79b8a5e 100644
--- a/lib/web_ui/test/engine/semantics/semantics_test.dart
+++ b/lib/web_ui/test/engine/semantics/semantics_test.dart
@@ -51,6 +51,9 @@ void runSemanticsTests() {
   group('Role managers', () {
     _testRoleManagerLifecycle();
   });
+  group('Text', () {
+    _testText();
+  });
   group('container', () {
     _testContainer();
   });
@@ -718,6 +721,74 @@ void _testLongestIncreasingSubsequence() {
   });
 }
 
+void _testText() {
+  test('renders a piece of plain text', () async {
+    semantics()
+      ..debugOverrideTimestampFunction(() => _testTime)
+      ..semanticsEnabled = true;
+
+    final ui.SemanticsUpdateBuilder builder = ui.SemanticsUpdateBuilder();
+    updateNode(
+      builder,
+      label: 'plain text',
+      rect: const ui.Rect.fromLTRB(0, 0, 100, 50),
+    );
+    owner().updateSemantics(builder.build());
+
+    expectSemanticsTree(
+      owner(),
+      '''<sem role="text" style="$rootSemanticStyle">plain text</sem>''',
+    );
+
+    final SemanticsObject node = owner().debugSemanticsTree![0]!;
+    expect(node.primaryRole?.role, PrimaryRole.generic);
+    expect(
+      node.primaryRole!.secondaryRoleManagers!.map((RoleManager m) => m.runtimeType).toList(),
+      <Type>[
+        Focusable,
+        LiveRegion,
+        RouteName,
+        LabelAndValue,
+      ],
+    );
+    semantics().semanticsEnabled = false;
+  });
+
+  test('renders a tappable piece of text', () async {
+    semantics()
+      ..debugOverrideTimestampFunction(() => _testTime)
+      ..semanticsEnabled = true;
+
+    final SemanticsTester tester = SemanticsTester(owner());
+    tester.updateNode(
+      id: 0,
+      hasTap: true,
+      label: 'tappable text',
+      rect: const ui.Rect.fromLTRB(0, 0, 100, 50),
+    );
+    tester.apply();
+
+    expectSemanticsTree(
+      owner(),
+      '''<sem flt-tappable="" role="text" style="$rootSemanticStyle">tappable text</sem>''',
+    );
+
+    final SemanticsObject node = owner().debugSemanticsTree![0]!;
+    expect(node.primaryRole?.role, PrimaryRole.generic);
+    expect(
+      node.primaryRole!.secondaryRoleManagers!.map((RoleManager m) => m.runtimeType).toList(),
+      <Type>[
+        Focusable,
+        LiveRegion,
+        RouteName,
+        LabelAndValue,
+        Tappable,
+      ],
+    );
+    semantics().semanticsEnabled = false;
+  });
+}
+
 void _testContainer() {
   test('container node has no transform when there is no rect offset',
       () async {