In the interaction between rubber tire and granular terrain, the dynamic behavior of granular terrain is significantly affected not only by the shape of soil grains, but also by the deformation contact of tread rubber. Therefore, the effect of these two factors should be considered in tire–sand interactions. In this study, an improved contact model including the effect of sand grain shape and tread rubber deformation is developed for dealing with the interaction between rubber tire and sand terrain. In sand–sand contact model, the interaction between sand grains takes the form of surface contact instead of conventional point contact, where the contact calculation contains four interactions, i.e., normal force, tangential force, rolling resistance and twisting resistance. And in tread–sand contact model, the contact between tread rubber and sand grains is surface contact, which includes the rolling resistance and twisting resistance on the grains caused by rubber deformation during contact. As a result, the complete and realistic evaluation of contact forces is accomplished. Next, a comparison of sandpile simulation of coarse particles and experiment is carried out to verify the effectiveness of the sand–sand contact model. Finally, the novel contact model is applied to tire–sand interaction simulations and compared with the single-wheel experiments. The results indicate that the proposed contact model can be a powerful tool to simulate the interactions between rubber tire and sand terrain.