A well-known disadvantage of pneumatic tires is the cessation of the ability to work with mechanical damage through and determines the need to search for fundamentally new design solutions for automobile wheels to increase the safety of automobiles and the survivability of wheeled vehicles. One such solution is the use of airless tires made of elastic polymeric materials. The Department of Mechanical Engineering and Transport of the Bratsk State University has developed full-scale models of wheels with airless tires made of elastic polyurethanes of Russian production for a car. The theoretical evaluation of the resilientible properties, load capacity and force heterogeneity of the experimental models was carried out by the finite element method. Electronic solid-state geometric models of airless tires have been created. Attributes of electronic models correspond to the nominal parameters of the physical models of automobile wheels. Nonlinear elastic isotropic models of polyurethane elastomers were adopted for nonlinear static analysis. The characteristics of the normal suppleness of airless tires and the graphs of oscillations of normal force with constant normal deflection in different positions of the wheels relative to their central transverse planes are the results of finite element modeling and calculation. Theoretical research results may be claimed by manufacturers of wheeled vehicles and tractors, construction and road vehicles, special motor vehicles and wheeled planetary rovers.