The use of high-power railway vehicles requires enhanced control of wheel-rail adherence. The aim of the present work is to prove the appropriateness of non-smooth models in the study of the axle torsional stick-slip vibrations which may occur when traction vehicles are set into motion. The model is simple, observes the main friction characteristics and provides the basis for efficient dynamics simulation. A set-valued friction law is accounted for and the motion equations are formulated as a switch model. Numerical integration is done by an event-driven algorithm. Application examples are presented. An experimental setup comprising a reduced-scale wheel set is analysed to validate the model proposed. The friction parameters are then identified using the proposed force-creepage relationship. Validation and verification are further carried out in frequency domain. Related problems may be solved using the present method, as it is pointed out in the paper.