A new nonlinear hysteretic model with considering the loading, unloading, and reloading processes is developed based on Drucker—Prager yield criterion and finite-element analysis. This model can be used for multiple repeated elastic—plastic normal direction contact problems between two identical spherical geomaterials. After examining the influence of material properties, strain hardening, and loading histories, we found that the hysteretic phenomena (represented by residual displacement and plastic work) become weak after the first cycle, and the subsequent cycles step into elastic shakedown state eventually. A critical number of cycles can be used to estimate the state of ratchetting, plastic shakedown, as well as elastic shakedown. It also found that the subsequent curves will be stiffer than the previous ones, especially when the yield strength is high and ratchetting effect is not strong. This new model can be used for a wide range of geomaterials under different loading levels, and it can also be extended to describe the constitutive behavior of spheres under earthquake as well as aftershocks.