diff --git a/src/Rules/Methods/CallMethodsRule.php b/src/Rules/Methods/CallMethodsRule.php
index b0d522f439..0bc36dff83 100644
--- a/src/Rules/Methods/CallMethodsRule.php
+++ b/src/Rules/Methods/CallMethodsRule.php
@@ -8,7 +8,10 @@
 use PHPStan\Internal\SprintfHelper;
 use PHPStan\Reflection\ParametersAcceptorSelector;
 use PHPStan\Rules\FunctionCallParametersCheck;
+use PHPStan\Rules\IdentifierRuleError;
 use PHPStan\Rules\Rule;
+use PHPStan\Type\Constant\ConstantStringType;
+use function array_map;
 use function array_merge;
 
 /**
@@ -31,12 +34,33 @@ public function getNodeType(): string
 
 	public function processNode(Node $node, Scope $scope): array
 	{
-		if (!$node->name instanceof Node\Identifier) {
-			return [];
+		if ($node->name instanceof Node\Identifier) {
+			$methodNames = [$node->name->name];
+		} else {
+			$methodNames = array_map(
+				static fn (ConstantStringType $constantString): string => $constantString->getValue(),
+				$scope->getType($node->name)->getConstantStrings(),
+			);
+			if ($methodNames === []) {
+				return [];
+			}
 		}
 
-		$methodName = $node->name->name;
+		foreach ($methodNames as $methodName) {
+			$errors = $this->processMethod($methodName, $node, $scope);
+			if ($errors !== []) {
+				return $errors;
+			}
+		}
+
+		return [];
+	}
 
+	/**
+	 * @return list<IdentifierRuleError>
+	 */
+	private function processMethod(string $methodName, MethodCall $node, Scope $scope): array
+	{
 		[$errors, $methodReflection] = $this->methodCallCheck->check($scope, $methodName, $node->var);
 		if ($methodReflection === null) {
 			return $errors;
diff --git a/src/Rules/Methods/CallStaticMethodsRule.php b/src/Rules/Methods/CallStaticMethodsRule.php
index 0f98eca2d9..b2ed84b209 100644
--- a/src/Rules/Methods/CallStaticMethodsRule.php
+++ b/src/Rules/Methods/CallStaticMethodsRule.php
@@ -8,7 +8,10 @@
 use PHPStan\Internal\SprintfHelper;
 use PHPStan\Reflection\ParametersAcceptorSelector;
 use PHPStan\Rules\FunctionCallParametersCheck;
+use PHPStan\Rules\IdentifierRuleError;
 use PHPStan\Rules\Rule;
+use PHPStan\Type\Constant\ConstantStringType;
+use function array_map;
 use function array_merge;
 use function sprintf;
 
@@ -32,11 +35,33 @@ public function getNodeType(): string
 
 	public function processNode(Node $node, Scope $scope): array
 	{
-		if (!$node->name instanceof Node\Identifier) {
-			return [];
+		if ($node->name instanceof Node\Identifier) {
+			$methodNames = [$node->name->name];
+		} else {
+			$methodNames = array_map(
+				static fn (ConstantStringType $constantString): string => $constantString->getValue(),
+				$scope->getType($node->name)->getConstantStrings(),
+			);
+			if ($methodNames === []) {
+				return [];
+			}
 		}
-		$methodName = $node->name->name;
 
+		foreach ($methodNames as $methodName) {
+			$errors = $this->processMethod($methodName, $node, $scope);
+			if ($errors !== []) {
+				return $errors;
+			}
+		}
+
+		return [];
+	}
+
+	/**
+	 * @return list<IdentifierRuleError>
+	 */
+	private function processMethod(string $methodName, StaticCall $node, Scope $scope): array
+	{
 		[$errors, $method] = $this->methodCallCheck->check($scope, $methodName, $node->class);
 		if ($method === null) {
 			return $errors;
diff --git a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
index 7342c880fe..eb39bbe703 100644
--- a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
@@ -3412,4 +3412,26 @@ public function testBug1953(): void
 		]);
 	}
 
+	public function testBug2920(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkNullables = true;
+		$this->checkUnionTypes = true;
+		$this->checkExplicitMixed = true;
+		$this->analyse([__DIR__ . '/data/bug-2920.php'], [
+			[
+				'Call to an undefined method Bug2920MethodCall\HelloWorld::a().',
+				13,
+			],
+			[
+				'Parameter #1 $s of method Bug2920MethodCall\HelloWorld::b() expects string, int given.',
+				14,
+			],
+			[
+				'Parameter #1 $s of method Bug2920MethodCall\HelloWorld::b() expects string, int given.',
+				17,
+			],
+		]);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
index c3842d461b..2bb7db8822 100644
--- a/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
@@ -852,4 +852,26 @@ public function testBug10872(): void
 		$this->analyse([__DIR__ . '/data/bug-10872.php'], []);
 	}
 
+	public function testBug2920(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkExplicitMixed = true;
+		$this->checkImplicitMixed = true;
+
+		$this->analyse([__DIR__ . '/data/bug-2920b.php'], [
+			[
+				'Call to an undefined static method Bug2920bStaticCall\HelloWorld::a().',
+				13,
+			],
+			[
+				'Parameter #1 $s of static method Bug2920bStaticCall\HelloWorld::b() expects string, int given.',
+				14,
+			],
+			[
+				'Parameter #1 $s of static method Bug2920bStaticCall\HelloWorld::b() expects string, int given.',
+				17,
+			],
+		]);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Methods/data/bug-2920.php b/tests/PHPStan/Rules/Methods/data/bug-2920.php
new file mode 100644
index 0000000000..1f76e4cc5d
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-2920.php
@@ -0,0 +1,26 @@
+<?php
+
+namespace Bug2920MethodCall;
+
+
+class HelloWorld
+{
+	public function sayHello(): void
+	{
+		$a = 'a';
+		$b = 'b';
+
+		$this->$a();
+		$this->$b(1);
+		$this->$b("1");
+
+		$this->b(1);
+		$this->b("1");
+	}
+
+	public function b(string $s): void
+	{
+	}
+
+}
+
diff --git a/tests/PHPStan/Rules/Methods/data/bug-2920b.php b/tests/PHPStan/Rules/Methods/data/bug-2920b.php
new file mode 100644
index 0000000000..9e88bbfa19
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-2920b.php
@@ -0,0 +1,26 @@
+<?php
+
+namespace Bug2920bStaticCall;
+
+
+class HelloWorld
+{
+	public function sayHello(): void
+	{
+		$a = 'a';
+		$b = 'b';
+
+		self::$a();
+		self::$b(1);
+		self::$b("1");
+
+		self::b(1);
+		self::b("1");
+	}
+
+	static public function b(string $s): void
+	{
+	}
+
+}
+