||The present paper is devoted to the study of the mechanical behavior of an Ethylene Propylene Diene Monomer (EPDM) rubber reinforced by polypropylene (PP) particles, revealed as compressible. The hyperlastic behavior of this blend has been characterized under cyclic uni-axial tensile tests. The experimental results show a significant effect of the fraction of (PP) particles (5%, 10%, 25% and 30% by weight) on the macroscopic behavior of the composite. In order to model this behavior, we first develop and implement a micromechanically-based nonlinear model for hyperelastic composites. The approach is based on the second order homogenization method proposed by Ponte Castaneda and Tiberio (2000) and for which suitable energy densities are adopted for the matrix and the inclusions phases, both assumed as compressible. We then proceed to the model verification by comparison with Finite Element simulations on a unit cell. Finally, we propose an extension of the model in order to take into account damage due to voids growth phenomena. The comparison of the multiscale damage model predictions with the experimental data obtained on the EPDM/PP composite indicates a very good agreement.