Efficient navigation of off-road vehicles heavily relies on the ability to accurately model the interaction between the vehicle and the terrain. One of the most important parts of this interaction is the deformation of the terrain and the tire. Although high-precision methods like finite element method (FEM) simulation can be used for this purpose, they require significant computational power, which is impractical to install in a vehicle for real-time navigation purposes. Therefore, simplified and less-detailed models are essential for on-board installation in real-time applications. In this study, three two-dimensional static terrain–vehicle models are compared to a detailed FEM reference model, and the results are evaluated both from the perspective of accuracy and computational capacity requirements. The analysis sheds light on the effectiveness of each model in the real-time navigation of off-road vehicles.