An air filter has a filter housing and a filter element inserted in the interior of the filter housing. The filter element has an inflow surface and an outflow surface and a filter medium that extends between inflow and outflow surfaces. The filter element has a circumferentially extending seal arranged in the area of the inflow surface or outflow surface and interacting in the mounting position with the sealing surface of the filter housing to separate inlet and outlet of the air filter. A support device clamps the filter element transversely to the insertion direction in the filter housing by a transverse clamping action in a support area that is spaced from the seal. The transverse clamping action results by an insertion movement of the filter element into the filter housing by interaction of the filter element with inner sides of the filter housing.