The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.