Some criteria are presented for evaluating the various tire design theories that are based on the equilibrium shape of the sidewall and on the rolling contour of a tire (RCOT). Tire failure types and the mathematical models by which they can be predicted by modern theories of rubber/cord fatigue are also described. A tire design theory based on stress‐strain optimization of its elements is proposed as is a hierarchic system of complicated tire models for calculation of stress‐strain cycles. Approaches are suggested for estimating fatigue strength of rubber‐cord composites. Influence of the cross‐section geometry and of the inner structure of the tire on stress‐strain cycles in the belt and bead of radial tires is investigated. Results obtained with the different design theories are compared.