Rubber dampers are widely used to damp out vibrations generated in many mechanical elements because of the excellent damping characteristics of rubber. The damping characteristics of rubber is much dependent on temperature and frequency, which, in some cases, limit the effectiveness of rubber dampers. In this study, in order to increase the damping properties and axial and cross stiffnesses of rubber vibration dampers which are used in recording and regenerating devices, solid cores were inserted with interference tolerance in the rubber dampers. The damping characteristics of the rubber dampers with cores were investigated by experimentally and numerically using finite element method with respect to the interference tolerance, the core roughness, the materials of the core and the environmental temperature. From the experimental and theoretical investigations, it was found that the core in the rubber increased both the damping and stiffness of the damper. Also, it was found that the damping and stiffness of the rubber damper were much dependent on the temperature and frequency. Using the results of the experimental and theoretical investigations, the optimum design method for the cored rubber damper for recording and regenerating devices was developed.