Cylindrical vibration damping apparatus and method of manufacturing the same

A cylindrical vibration damping apparatus having an elastic body connecting an inner shaft and an outer cylinder member, and a pair of rubber stop plates disposed at axial ends of the inner shaft member. Each rubber stop plate has a mount hole that fits about the outside of the inner shaft member. Pairs of mating projections and mating recesses are provided to an interface between an inner circumferential surface of the mount hole of the each rubber stop plate and an outer circumferential surface of the corresponding axial end of the inner shaft member at three or more different intervals in a circumferential direction so that the pair of rubber stop plates are installed onto the axial ends of the inner shaft member with correct identification of a front and back and a circumferential position about the inner shaft member. A method of manufacturing the same is also disclosed.