SUMMARYThis paper describes a methodology to build equivalent continuum (ECC) models to represent jointed media for non-linear wave propagation. In the present work, we study the response of randomly jointed rock media both to quasi-static and dynamic loadings. We have found that, unlike in the quasi-static case where no relaxation is observed, during dynamic loading, the deviatoric stress drops in the plastic wave after reaching its peak. Such stress relaxation phenomenon is calculated in jointed media, although the model used for intact rock blocks is rate-independent. This is a strong indication that EC models for jointed rock should include some rate-dependence when used in wave propagation simulations.