The problem or rolling contact is of a great interest from the practical and cognitive points of view. It concerns for example a wheel passage on a rail, as well as many other processes where rolling or rolling with sliding is involved. Particularly, residual stresses distributions in the subsurface area due to plastic deformations are of significant importance: these stresses strongly influence fatigue limit and cracking tendencies of the material. A motion of the wheel on the rail (or of a roller on a strip) often has a very complex character: it consists of rolling, sliding in the longitudinal direction due to brakings and accelerations, sliding in the transversal direction, etc. Investigations conducted on this field by many authors have not yet delivered a unique solution. The aim of this paper is to determine the influence of some of these components of the wheel motion (separately and in common action) on residual stresses distributions. The problem has been investigated numerically by the FEM method, using the program SEGLA developed by the authors. The program can be applied to solving linear and nonlinear 2D, axisymmetric and 3D problems with elasto-plastic effects in the nonlinear contact and fracture mechanics. It uses three, four, six, eight and nine-node elements and also the special “spring” elements to model contact. The applied algorithm allows automatic analysis of these fragments of boundary, which enter and leave the contact; in the area where the “new” contact is created the program introduces additional elements.