A vibration damping device having a stopper structure includes: a rubber
elastic body of generally frustoconical configuration overall; a first
mounting member formed independently of the rubber elastic body, and
directly or indirectly superimposed on the rubber elastic body in an
external load input direction; and a second mounting member including a
cylindrical portion that is bonded to a large diameter side outer
circumferential surface of the rubber elastic body. A first and second
abutting portions of the first and second mounting members are situated
to be opposed to each other in a rebound direction with a given distance
interposed therebetween, and a stop rubber is disposed between the first
and second abutting portions so that the first and second abutting
portions come into abutting contact with each other in a cushion-wise
fashion, via the stop rubber to thereby provide a stopper structure.