In a method applicable to a vibration damping engine mount for an internal combustion engine and the vibration damping engine mount therefor, a varying air pressure is supplied to the vibration controllable support mechanism and one of a negative pressure developed in a negative pressure pump and the atmospheric pressure to the vibration controllable support mechanism is supplied to a vibration controllable support mechanism constituting the vibration damping engine mount in accordance with the vibration of the internal combustion engine.