A torsional vibration damper or other vibration damping device with a rubber vibration absorbing element. The rubber element is a peroxide-cured composition comprising 100 parts of ethylene-alpha-olefin elastomer, and 20 to 100 parts of substantially isobutylene or butene polymer having a viscosity average molecular weight greater than about 5000. The polymer may also be a copolymer of isobutylene and isoprene. The addition of the isobutylene polymer to the ethylene-alpha-olefin elastomer composition increases the vibration damping character of the rubber.