A torsional vibration damper has an input hub and an output hub drivingly connected by a plurality of elastomeric band support members and an elastomeric band. The support members are maintained in contact with at least one of the hubs by the elastomeric band. The band permits relative angular movement between the hubs in response to a camming action which is transmitted to the elastomeric band by the support members. The relative angular displacement between the input and output members increases as the base level of torque transmission increases while slight relative movements from the base torque level setting are operative to attenuate and dampen the torsional disturbances which are imposed on the input hub by a prime mover such as an internal combustion engine.