In a vibration damping apparatus for supporting an engine on a vehicular body, an elastic member damps a vibration developed from the engine, a stopper is brought in contact with the elastic member to limit a transmission of a fluctuation developed on the engine therethrough, and a vehicular body support member integrated with the elastic member to fix the elastic member on the vehicular body, the elastic member including a stopper fixing portion placed at a first position opposite to a second position faced toward the engine to fix the stopper at the first position and the stopper including a bending portion, one side thereof with respect to the bending portion being fixed onto the engine and the other side thereof with respect thereto being fixed onto the stopper fixing portion of the elastic member so as to grasp the elastic member between both sides of the stopper.