Vehicle movement on unpaved surfaces is important to military, agriculture, forestry, mining, construction, and recreation industries. Because of the complicated nature of vehicle-terrain interaction, comprehensive modeling of off-road mobility is often done using empirical algorithms. The desire to incorporate more physics into performance models has generated great interest in applying numerical modeling techniques in a full three-dimensional analysis, accounting for the deformation of both the tire and the terrain. In this study, a three-dimensional finite element model was constructed to simulate a tire rolling over snow. The snow was modeled as an inelastic material using critical-state constitutive modeling and plasticity theory. The snow material model was generated from experiments on the mechanical deformation of snow and was validated using a plate sinkage test. The tire models represent a range of sizes accommodating light-truck and off-road military vehicles and were rolled on snow of various depths. The combined tire-terrain models were validated using force measurements collected with instrumented vehicles and with measured snow deformation. The model results were also compared to vehicle mobility predictions made using the winter algorithms of the NATO Reference Mobility Model. These comparisons illustrate the agreement between the finite element models and field measurements of motion resistance forces and snow deformation under the tire.