Purpose: Investigation of stresses on contact surface during interaction of a railway wheel and rail from normal pressure and tangential forces in the presence of adhesion and sliding zones of different sizes. Methods: Formulas for equivalent and tangential stresses for plane deformation and plane stress state are given and used for calculations. Special attention is paid to the study of stress state at contact boundary points of cylinders, which parameters are calculated for at contact surface points at boundary between sliding and adhesion zones. Results: The study of the distribution of equivalent stresses in the zone of their maximal values is carried out, the dependence from friction coefficients is established. The distribution of stresses on contact surface of a drive cylinder from normal pressure and from contact tangential forces in the presence of adhesion and slippage zones for different ratios between them is shown. The obtained results revealed the increase in stresses at the boundaries of sliding and adhesion sections, the effect of absence of tangential forces or presence of complete slippage. Practical importance: The data make it possible to predict more accurately a decrease in the contact-fatigue durability of samples and can be useful in studying the appearance of microcracks of a wheel or rail during their interaction. Physical modeling of the interaction of rolling elements, such as a rail and a wheel, which is performed at actual work loads, interaction speeds, various friction coefficients, at sliding or adhesion recreates with certain reliability actual conditions of interaction of a wheel and a rail, and the results help to predict the reliability of a wheel-rail pair in railway transport.