Transfer of the load from the wheels on the rail occurs at a very small area compared with the size of the wheels and rails. The materials near this site have a very large voltage. Determination of contact stresses is complicated by the fact that the magnitude of these stresses in the rails under actually revolving wheel load exceeds the yield and compressive strength of modern rail steel. We should note that the metal of the rail head, experiencing contact stresses, especially when the location of the pads is closer to the middle of the rail head, works in the conditions close to the compression conditions, and therefore can withstand higher voltage without plastic deformation than the standard compressible sample. But, as a rule, the observed hardening of the metal in the zone of contact stresses and lapping at the edges of the rail head indicates the presence of plastic deformation and, consequently, higher stresses in the wheel-rail contact zone than the yield strength of the metal rail even in the conditions of its operation in the rail head.The use of the design equations derived on the basis of the Hertz theory for metal behavior in elastic stage, is valid. The reason is that each individual dynamic application of wheel loads on the rail is very short, and the residual plastic deformation from the individual loads of the pair of wheels on the rail is actually small. This elastic-plastic deformation of the rail becomes visible as a result of gradual gaining of a missed tonnage of rails and wheels respectively. Irregularities on the running surface of the wheels are of two types. The most common are the so-called continuous bumps on the wheel, when due to the uneven wear of rail the original shape of the wheel across the tread surface distorts. But nowadays, more and more often there occur isolated smooth irregularities of the wheel pairs, due to the increased wear of the wheel because of the stopping and blocking of wheels of the vehicles - slides (potholes), etc.The motion of the wheels with irregularities on the surface of the rail leads to vertical oscillation of the wheel, resulting in the forces of inertia, which is an additional load on the rail. In case of movement of the wheel with isolated roughness on the tread surface of the slide there is a strike, having a very large additional impact on the rail. Such attacks can cause kinked rails, especially in the winter months when there is increased fragility of rail steel, because of lowered temperatures. This is an abnormal phenomenon and occurs relatively rarely, at a small number of isolated irregularities on a wheel of the rolling stock. As correlations connecting the contact force and local deformation in the interaction of the wheel-rail system, we use the quasi-static Hertz’s model, linear-elastic model and two elastoplastic contact models: Alexandrov-Kadomtsev and Kil’chevsky. According to the results of Loktev’s studies ratios of the contact Hertz’s theory are quite suitable for modeling the dynamic effects of wheel and rail for speeds up to 90 km/h for engineering calculations. Since the contact surface is homogeneous and isotropic, the friction forces in the contact zone are not taken into account, the size of the pad is small compared to the dimensions of the contacting bodies and characteristic radii of curvature of the undeformed surfaces, the contacting surfaces are smooth.When train is driving, the position of the wheelset in relation to the rails varies considerably, giving rise to different combinations of the contact areas of the wheel and rail. Even assuming constant axial load the normal voltage will vary considerably because of the differences in the radii of curvature of the contacting surfaces of these zones. Thus, the proposed method allows evaluating the influence of several types of wheel defects on the condition of the rail and the prospects of its use in the upper structure of a railway track on plots with different speed and traffic volumes. Also the results can be used to solve the inverse of the considered problems, for example, when designing high-speed highways, when setting the vehicle speed and axle load, and the solution results are the parameters of the defects, both wheelsets and the rails, in case of which higher requirements for the safe operation of railways are observed.