Among the large number of studies aimed at solving the problems of determining the kinematic and force characteristics of a wheel when it rolls under various operating conditions, one can highlight analytical works based on the mechanics of interaction of an elastic wheel with a supporting surface. This approach used in this article, from the analysis of the phenomena occurring in the contact of an elastic wheel with a rigid base, makes it possible to consider general issues of the mechanics of wheel rolling. This made it possible to obtain for the considered friction pair “elastic wheel – supporting surface” relatively simple dependencies that make it possible to determine the longitudinal force and power of friction losses in contact, the relative speed loss (slippage) of the wheel, the coordinate of the boundary of the adhesion and sliding areas on the contact area, the drag coefficient rolling, the coefficient of tangential elasticity of the wheel, evaluate the legality of using various accepted laws of pressure distribution in contact.