The contemporary striving for increased speed in rail transport, with simultaneous requirements in terms of travel comfort, makes the safety of rail vehicles one of the priorities in the process of passenger rail transport. It is obvious that safety in this case is determined by: the technical condition of the vehicle, the condition of the railway infrastructure and the conditions of cooperation between the railway vehicle and the track. Railway vehicles running safety tests can be carried out on-line, in real operating conditions, and off-line with the use of mathematical models and simulation methods. The on-line research does not assess the impact of the parameter characterizing the track geometry, i.e., rail inclination, on the driving safety, and the deviation of the shape of wheel and rail running surfaces from the nominal dimensions is rarely diagnosed and taken into account in the tests. The considerations in this article are devoted to the discussion of the effects on the safety of a rail vehicle, resulting from possible changes in the inclination of the rails and deviations of the rail profile from the nominal dimensions. The research, the results of which are presented in the article, were carried out using off-line methods for the wheelset, using mathematical models, but taking into account the forces resulting from the interactions of the bogie frame and the railway wagon body and the real track geometry.