A three‐dimensional prediction model has been developed in which the interaction between snow and a rolling tire with tread pattern is considered. An explicit finite element method (FEM) and a finite volume method (FVM) are used to model tire and snow respectively. Snow deformation is calculated by the Eulerian formulation to solve the complex interaction between snow and tire tread pattern. Coupling between a tire and snow is automatically computed by the coupling element. Numerical modeling of snow is essential to the tire performance prediction on snow. In this study, snow is assumed to be homogeneous and considered to be an elasto‐plastic material. The Mohr‐Coulomb yield model, in which the yield stress is a single function of pressure, is adopted. This function is investigated by tire traction tests under a wide range of tire contact pressures using several tires with different inflation pressures and patterns. The predicted results using the Mohr‐Coulomb yield model are compared with those using the Capped Drucker‐Pragger and the Cam‐Clay yield models. Snow traction of a tire featuring different tread patterns is simulated by this technology. Results are shown to be in good qualitative agreement with experimental data.