diff --git a/packages/flutter/lib/src/material/calendar_date_picker.dart b/packages/flutter/lib/src/material/calendar_date_picker.dart
index e39fba6af50..d203a96cadd 100644
--- a/packages/flutter/lib/src/material/calendar_date_picker.dart
+++ b/packages/flutter/lib/src/material/calendar_date_picker.dart
@@ -409,6 +409,7 @@ class _DatePickerModeToggleButtonState extends State<_DatePickerModeToggleButton
               label: MaterialLocalizations.of(context).selectYearSemanticsLabel,
               excludeSemantics: true,
               button: true,
+              container: true,
               child: SizedBox(
                 height: _subHeaderHeight,
                 child: InkWell(
diff --git a/packages/flutter/lib/src/material/date_picker.dart b/packages/flutter/lib/src/material/date_picker.dart
index 8b5aadbe911..cf75c91d10f 100644
--- a/packages/flutter/lib/src/material/date_picker.dart
+++ b/packages/flutter/lib/src/material/date_picker.dart
@@ -861,64 +861,76 @@ class _DatePickerHeader extends StatelessWidget {
 
     switch (orientation) {
       case Orientation.portrait:
-        return SizedBox(
-          height: _datePickerHeaderPortraitHeight,
-          child: Material(
-            color: backgroundColor,
-            child: Padding(
-              padding: const EdgeInsetsDirectional.only(
-                start: 24,
-                end: 12,
-                bottom: 12,
-              ),
-              child: Column(
-                crossAxisAlignment: CrossAxisAlignment.start,
-                children: <Widget>[
-                  const SizedBox(height: 16),
-                  help,
-                  const Flexible(child: SizedBox(height: 38)),
-                  Row(
-                    children: <Widget>[
-                      Expanded(child: title),
-                      if (entryModeButton != null)
-                        entryModeButton!,
-                    ],
-                  ),
-                ],
+        return Semantics(
+          container: true,
+          child: SizedBox(
+            height: _datePickerHeaderPortraitHeight,
+            child: Material(
+              color: backgroundColor,
+              child: Padding(
+                padding: const EdgeInsetsDirectional.only(
+                  start: 24,
+                  end: 12,
+                  bottom: 12,
+                ),
+                child: Column(
+                  crossAxisAlignment: CrossAxisAlignment.start,
+                  children: <Widget>[
+                    const SizedBox(height: 16),
+                    help,
+                    const Flexible(child: SizedBox(height: 38)),
+                    Row(
+                      children: <Widget>[
+                        Expanded(child: title),
+                        if (entryModeButton != null)
+                         Semantics(
+                          container: true,
+                          child: entryModeButton,
+                        ),
+                      ],
+                    ),
+                  ],
+                ),
               ),
             ),
           ),
         );
       case Orientation.landscape:
-        return SizedBox(
-          width: _datePickerHeaderLandscapeWidth,
-          child: Material(
-            color: backgroundColor,
-            child: Column(
-              crossAxisAlignment: CrossAxisAlignment.start,
-              children: <Widget>[
-                const SizedBox(height: 16),
-                Padding(
-                  padding: const EdgeInsets.symmetric(
-                    horizontal: _headerPaddingLandscape,
-                  ),
-                  child: help,
-                ),
-                SizedBox(height: isShort ? 16 : 56),
-                Expanded(
-                  child: Padding(
+        return Semantics(
+          container: true,
+          child:SizedBox(
+            width: _datePickerHeaderLandscapeWidth,
+            child: Material(
+              color: backgroundColor,
+              child: Column(
+                crossAxisAlignment: CrossAxisAlignment.start,
+                children: <Widget>[
+                  const SizedBox(height: 16),
+                  Padding(
                     padding: const EdgeInsets.symmetric(
                       horizontal: _headerPaddingLandscape,
                     ),
-                    child: title,
+                    child: help,
                   ),
-                ),
-                if (entryModeButton != null)
-                  Padding(
-                    padding: const EdgeInsets.symmetric(horizontal: 4),
-                    child: entryModeButton,
+                  SizedBox(height: isShort ? 16 : 56),
+                  Expanded(
+                    child: Padding(
+                      padding: const EdgeInsets.symmetric(
+                        horizontal: _headerPaddingLandscape,
+                      ),
+                      child: title,
+                    ),
                   ),
-              ],
+                  if (entryModeButton != null)
+                    Padding(
+                      padding: const EdgeInsets.symmetric(horizontal: 4),
+                      child: Semantics(
+                        container: true,
+                        child: entryModeButton,
+                      ),
+                    ),
+                ],
+              ),
             ),
           ),
         );
diff --git a/packages/flutter/lib/src/material/input_date_picker_form_field.dart b/packages/flutter/lib/src/material/input_date_picker_form_field.dart
index 6341360da68..62210d6d49b 100644
--- a/packages/flutter/lib/src/material/input_date_picker_form_field.dart
+++ b/packages/flutter/lib/src/material/input_date_picker_form_field.dart
@@ -256,21 +256,24 @@ class _InputDatePickerFormFieldState extends State<InputDatePickerFormField> {
       ?? theme.inputDecorationTheme.border
       ?? (useMaterial3 ? const OutlineInputBorder() : const UnderlineInputBorder());
 
-    return TextFormField(
-      decoration: InputDecoration(
-        hintText: widget.fieldHintText ?? localizations.dateHelpText,
-        labelText: widget.fieldLabelText ?? localizations.dateInputLabel,
-      ).applyDefaults(inputTheme
-        .merge(datePickerTheme.inputDecorationTheme)
-        .copyWith(border: effectiveInputBorder),
+    return Semantics(
+      container: true,
+      child: TextFormField(
+        decoration: InputDecoration(
+          hintText: widget.fieldHintText ?? localizations.dateHelpText,
+          labelText: widget.fieldLabelText ?? localizations.dateInputLabel,
+        ).applyDefaults(inputTheme
+          .merge(datePickerTheme.inputDecorationTheme)
+          .copyWith(border: effectiveInputBorder),
+        ),
+        validator: _validateDate,
+        keyboardType: widget.keyboardType ?? TextInputType.datetime,
+        onSaved: _handleSaved,
+        onFieldSubmitted: _handleSubmitted,
+        autofocus: widget.autofocus,
+        controller: _controller,
+        focusNode: widget.focusNode,
       ),
-      validator: _validateDate,
-      keyboardType: widget.keyboardType ?? TextInputType.datetime,
-      onSaved: _handleSaved,
-      onFieldSubmitted: _handleSubmitted,
-      autofocus: widget.autofocus,
-      controller: _controller,
-      focusNode: widget.focusNode,
     );
   }
 }
diff --git a/packages/flutter/test/material/date_picker_test.dart b/packages/flutter/test/material/date_picker_test.dart
index 177a79800e9..926e4598600 100644
--- a/packages/flutter/test/material/date_picker_test.dart
+++ b/packages/flutter/test/material/date_picker_test.dart
@@ -13,6 +13,7 @@ import 'package:flutter/foundation.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter/services.dart';
 import 'package:flutter_test/flutter_test.dart';
+import '../widgets/clipboard_utils.dart';
 
 void main() {
   TestWidgetsFlutterBinding.ensureInitialized();
@@ -1577,6 +1578,13 @@ void main() {
     });
 
     testWidgets('input mode', (WidgetTester tester) async {
+      // Fill the clipboard so that the Paste option is available in the text
+      // selection menu.
+      final MockClipboard mockClipboard = MockClipboard();
+      tester.binding.defaultBinaryMessenger.setMockMethodCallHandler(SystemChannels.platform, mockClipboard.handleMethodCall);
+      await Clipboard.setData(const ClipboardData(text: 'Clipboard data'));
+      addTearDown(() => tester.binding.defaultBinaryMessenger.setMockMethodCallHandler(SystemChannels.platform, null));
+
       final SemanticsHandle semantics = tester.ensureSemantics();
 
       initialEntryMode = DatePickerEntryMode.input;
@@ -1596,7 +1604,22 @@ void main() {
           isFocusable: true,
         ));
 
-        // The semantics of the InputDatePickerFormField are tested in its tests.
+        expect(tester.getSemantics(find.byType(EditableText)), matchesSemantics(
+          label: 'Enter Date',
+          isEnabled: true,
+          hasEnabledState: true,
+          isTextField: true,
+          isFocused: true,
+          value: '01/15/2016',
+          hasTapAction: true,
+          hasSetTextAction: true,
+          hasSetSelectionAction: true,
+          hasCopyAction: true,
+          hasCutAction: true,
+          hasPasteAction: true,
+          hasMoveCursorBackwardByCharacterAction: true,
+          hasMoveCursorBackwardByWordAction: true,
+        ));
 
         // Ok/Cancel buttons
         expect(tester.getSemantics(find.text('OK')), matchesSemantics(