A damping system for a gas turbine engine comprises a bearing mounted to a rotor shaft and a support connected to an outer race of the bearing. The support has a wall secured to a casing of the gas turbine engine at a connection portion. The wall has a first surface positioned against a surface of the casing with the first surface being in a non-parallel relation with the rotational axis of the rotor shaft. A cavity is defined in the first surface by a narrowing of a thickness of the wall. The cavity contains a damping fluid to dampen elastic deformation of the wall at the cavity resulting from axial oscillations of the rotor shaft. An abutment is provided to limit an amplitude of the elastic deformation of the wall.