Abstract: A vibration damping device (10) comprising an axisymmetric elastomeric body (20), which has a base side (40), a periphery (50), and a through hole (60). The body comprises an integrally bonded cup-shaped axisymmetric structure (70), which has a base portion (80), a side wall (90), and an opening (100) encompassing the through hole. The base portion and the side wall adjoin to the base side and periphery, respectively. The elastomeric body has a groove (110) encompassed by the side wall, which groove extends along and close to the periphery, and is adapted to receive a separately provided axisymmetric snubber member. A vibration damper assembly comprising two vibration-damping devices of said kind.