diff --git a/python/python-psi-impl/src/com/jetbrains/python/codeInsight/intentions/SpecifyTypeInPy3AnnotationsIntention.java b/python/python-psi-impl/src/com/jetbrains/python/codeInsight/intentions/SpecifyTypeInPy3AnnotationsIntention.java
index 806b2e41a2a1..30cb3c89bc85 100644
--- a/python/python-psi-impl/src/com/jetbrains/python/codeInsight/intentions/SpecifyTypeInPy3AnnotationsIntention.java
+++ b/python/python-psi-impl/src/com/jetbrains/python/codeInsight/intentions/SpecifyTypeInPy3AnnotationsIntention.java
@@ -92,7 +92,13 @@ public class SpecifyTypeInPy3AnnotationsIntention extends TypeIntention {
                                                    boolean createTemplate) {
     final PyExpression defaultParamValue = parameter.getDefaultValue();
 
-    final String paramName = StringUtil.notNullize(parameter.getName());
+    String paramName = StringUtil.notNullize(parameter.getName());
+    if (parameter.isPositionalContainer()) {
+      paramName = "*" + paramName;
+    }
+    else if (parameter.isKeywordContainer()) {
+      paramName = "**" + paramName;
+    }
     final PyElementGenerator elementGenerator = PyElementGenerator.getInstance(project);
 
     final String defaultParamText = defaultParamValue == null ? null : defaultParamValue.getText();
diff --git a/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter.py b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter.py
new file mode 100644
index 000000000000..6b6c62d5d83d
--- /dev/null
+++ b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter.py
@@ -0,0 +1,2 @@
+def fo<caret>o(**x):
+    pass
\ No newline at end of file
diff --git a/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter_after.py b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter_after.py
new file mode 100644
index 000000000000..be4b0bbae0ff
--- /dev/null
+++ b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionKeywordContainerParameter_after.py
@@ -0,0 +1,2 @@
+def foo(**x: object<caret>) -> object:
+    pass
\ No newline at end of file
diff --git a/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter.py b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter.py
new file mode 100644
index 000000000000..b653f48634ba
--- /dev/null
+++ b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter.py
@@ -0,0 +1,2 @@
+def fo<caret>o(*x, **y):
+    pass
\ No newline at end of file
diff --git a/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter_after.py b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter_after.py
new file mode 100644
index 000000000000..34c7f8cb394e
--- /dev/null
+++ b/python/testData/intentions/PyAnnotateTypesIntentionTest/functionPositionalAndKeywordContainerParameter_after.py
@@ -0,0 +1,2 @@
+def foo(*x: object<caret>, **y: object) -> object:
+    pass
\ No newline at end of file
diff --git a/python/testSrc/com/jetbrains/python/intentions/PyAnnotateTypesIntentionTest.java b/python/testSrc/com/jetbrains/python/intentions/PyAnnotateTypesIntentionTest.java
index 5d8a73fbae51..ef00da2c9ded 100644
--- a/python/testSrc/com/jetbrains/python/intentions/PyAnnotateTypesIntentionTest.java
+++ b/python/testSrc/com/jetbrains/python/intentions/PyAnnotateTypesIntentionTest.java
@@ -46,6 +46,16 @@ public class PyAnnotateTypesIntentionTest extends PyIntentionTestCase {
     doIntentionTest(PyPsiBundle.message("INTN.add.type.hints.for.function", "method"));
   }
 
+  // PY-41976
+  public void testFunctionKeywordContainerParameter() {
+    doTest();
+  }
+
+  // PY-41976
+  public void testFunctionPositionalAndKeywordContainerParameter() {
+    doTest();
+  }
+
   private void doTest() {
     doTest(PyPsiBundle.message("INTN.NAME.add.type.hints.for.function"), LanguageLevel.PYTHON34);
   }