The Mullins effect refers to a stress-softening phenomenon of rubber-like materials during cyclic loading. Anisotropy of the material behaviour is generally observed after stretching. In this paper, a large set of original suitable experiments are reported to characterise this effect under several deformation conditions. Then, a phenomenological model is derived to capture the anisotropic distribution. For that, the affine micro-sphere model (Miehe et al., 2004) is amended with a directional network alteration in order to describe anisotropy. The alteration process, involving the breakage and the slippage of the links embedded in the macromolecular network, is modeled by the evolution of the average number of monomer segments per chain during stretching. The average chain length and the chain density are incrementally described by functions to allow both softening and stiffening, depending to the maximum and the minimum stretch rates and levels endured in each direction. The good capacity of the model to reproduce experimental observations validates the above assumptions.