Purpose. Determination of the functional correlation between power (tangential reaction) and kinematic (relative slip) parameters during nonstationary rectilinear motion of the rail wheel along the rail. Methodology. An analytical model of the interaction between the wheel and rail on an elementary contact area taking into account the presence of normal and shearing load (thrust or braking mode) is developed. Using the analytical model, a qualitative relationship that reflects the features of the friction contact of a wheel-rail pair for various operating conditions is obtained considering the nature of the interaction of the contacting pair, which significantly differs. The mathematical description of the process is based on experimental studies of the dependence of the tractive force on the speed of relative motion (incomplete slippage - the so-called creep mode, failure of adhesion and total sliding, which leads to decrease in traction force) of D. K. Minov and A. A. Renhevych. Findings. On the basis of theoretical studies of the parameters of vehicle motion along the rail track, a mathematical model of the tangential reaction realization by wheel in the case of nonstationary rectilinear motion is formulated. The functional relationship between the power and kinematic parameters is established, which allows predicting the operational properties and solving the problems of the dynamics of rail transport with a higher degree of accuracy. Originality. Taking into account inelastic resistance of contacting bodies, analytical dependences are obtained to determine the current value of the force at the contact area upon the availability of longitudinal load. The interaction conditions under which the deformation can occur both within the elasticity of the materials of the contacting bodies and the violation of the surfaces contact are considered. Approximating dependences of tractive effort on the relative speed of wheel and rail movement are proposed for locomotives. Practical value. Knowledge of the processes occurring in the contact area while transferring the torque from the wheel of the locomotive to the rail will facilitate finding the correct solution to the problem of interaction between the wheel-rail system of mining rail transport in complex mining and geological operational conditions. It helps to increase the efficiency of torque transmission at the quasi-stationary mode of vehicle movement.