The ring on elastic foundation (REF) model has been used as a pneumatic tire analog for many types of two‐dimensional contact problems. This paper investigates the suitability of the model to reproduce hub forces during large deformation, quasi-static contact. Two types of tire contact problems are considered in this paper. The first problem is a tire deforming against a flat plate, and the second is a tire rolling over a 50 mm step. The REF model is implemented in a nonlinear, finite element program with elements that accommodate large deformation and contact. Experimental hub force measurements verify the simulation results. This paper shows that the best match with experimental data is accomplished with a model that consists entirely of beam elements and includes a softening foundation. Also, it shows that the hub force is strongly dependent on the radial stiffness of the foundation and the inflation pressure.