The goal of this communication is to formulate a phenomenological continuum model which extends to the inclusion of residual strains the pseudo-elastic model for the (idealized) Mullins effect presented by Ogden k Roxburgh (1999a). The proposed model is based on a strain-energy function describing the loading path and an additive damage function responsible for the unloading path. Three damage variables govern the anisotropic damage mechanism which is controlled by the evolution of the principal stretches. The pseudo-elastic model described has been implemented in a finite element program. Finally we demonstrate two representative examples: a simple tension test and an inhomogeneous tension test of a rubber strip showing analytical and finite element results.