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The statistical analysis performed on the defectiveness of rails in the Kiev subway railway shows that the main cause of the occurrence of most defects is the contact fatigue of the rail material. The paper presents modern concepts of crack growth in the railhead. It has been found that one of the most promising directions of studying the stress-strain state of rails and the crack growth process is a numerical simulation, which results on the contact interaction between rails and subway rolling stock wheels are presented. During the simulation, the problem was solved in an elastic formulation. We considered R50, R65, and UIC60 rail profiles, standard railway wheels, and wheels whose tire profile was developed by the Minetek closed joint-stock company. The conditions for the rail–wheel interaction corresponded to train movement on the straight section of the track without slipping. The effect of the wheel tire profile on the contact stress level in rails of different types has been assessed. Comparison of the maximum equivalent stress levels for a different combination of rail and wheel types shows that the best combination (in terms of reducing the contact stress level) for the straight sections of the subway track is an R50 rail with a gradient of 1 in 20 and 1 in 10 taper wheel, whose profile corresponds to GOST 9036-88. When wheels with the profile developed by the Minetek company are used, the maximum equivalent stress level in the contact zone is over 1000 MPa for all rail types. It is higher than the yield strength of rail steel, which will accelerate wear and give rise to low-cycle fatigue cracks with subsequent formation of contact fatigue defects. [ABSTRACT FROM AUTHOR]