Elastomers present a stress softening phenomenon known as the Mullins effect. The main difficulty is to determine a model based on physical hypothesis with an analytical form usable in finite element codes. An attempt to reconcile the two approaches is presented. The alteration model proposed by Marckmann et al. (2002) is successful in the simulation of the stress softening phenomenon but has a complex analytical form because of the eight-chain model formulation. Thanks to the use of equivalences between different hyperelastic energy densities, a new stress softening model is built thanks to the Gent hyperelastic energy density.