This work presents the results of a study carried out to characterize the mechanical response of a high damping rubber to be used in designing and constructing energy dissipating devices and base isolators for controling strong vibrations in civil engineering structures. A new parametric model of the elastomer is proposed to be employed in the design procedure and structural analysis of passive controlled structures. The parameters of the model are calibrated using experimental data obtained from tests on rubber specimens under different loading paths. The main dissipating energy mechanisms of the rubber are identified. The proposed model is able to reproduce those main mechanisms as well as geometric second order effects such as tension stiffening due to the effect of axial strains in the response. The response predicted by the proposed model is compared with that obtained from experimental tests and from the Kelvin and plasticity models.