Steel-concrete composite frames may make up efficient earthquake resistant structural systems due to the formation of plastic hinges. However the energy dissipation associated to the ductile behaviour of the dissipating zones induces a large amount of structural damages. According to recent design methods, an energy dissipation system may be added to the frame in order to reduce the damages to the acceptable limits imposed by the performance level of the structure in the case of strong motions. In this paper High Damping Rubber dissipation devices are considered. An analytical model of HDR dissipation devices is firstly de-scribed. Successively, the results of a numerical investigation regarding the seismic response of an elastic Single Degree of Freedom system coupled with an HDR dissipating device are reported in order to obtain useful information to design elastic structures that include HDR-based devices.