The object of the invention is to provide sound insulating members exhibiting both high vibration damping performance and high sound insulation performance, a vibration damping material for affording such members and a resin composition for forming the vibration damping material. The invention provides a first resin composition for vibration damping materials which contains 100 parts by weight of a chlorine-containing thermoplastic resin, and 20 to 200 parts by weight of a chlorinated paraffin having 12 to 16 carbon atoms on average. The thermoplastic resin contains preferably 20 to 70 wt. %, more preferably 30 to 70 wt. %, of chlorine. The chlorinated paraffin is preferably 30 to 70 wt. %, more preferably 35 to 65 wt. %, in chlorination degree.