<p>We propose a new analytical model for a reinforced tire that takes into account the mass of the sidewalls. The tire surface is represented by a flexible tread combined with elastic sidewalls. Using the Hamilton–Ostrogradsky variational principle, we derive the equations of motion and conditions on the unknown in advance boundary of contact area. We study the steady-state rolling of a loaded tire at constant speed on a plane without slipping. We determine all characteristics of the deformed tire, including the parameters that define its shape, the dimensions and position of the contact area, the components of the constraint reactions, and the tension in the tire tread. We also derive the relationships between external forces and torque applied to the wheel disk, and the conditions required for the steady-state rolling regime. Bibliography&#xa0;:&#xa0; 4 titles. Illustrations&#xa0;:&#xa0; 1</p>