Abstract: Stress softening, known as the Mullins effect, is observed in rubber-like materials after initial loading cycles. Experimental observations have shown that the Mullins effect leads to a permanent set and induces anisotropic properties. A multi-axial, compressible strain energy function based on the Hencky strain is proposed to account for the stress softening and simulate the permanent set and anisotropic properties by introducing two variables, separately characterizing the permanent set and anisotropic properties, which are dependent on dissipation. A comprehensive, explicit shape function is proposed by using the spherical coordinate system to make the model effective in arbitrary direction. The new model exhibits isotropic properties when it not yet induced stress softening, and becomes anisotropy when the Mullins effect occurs. The residual strain increases and reach a fixed value as the loading-unloading cycles proceeds, and the anisotropy becomes more obvious. The simulation results are shown good accord with the classical experimental data and successfully forecast the permanent set and anisotropic properties induced by stress softening.