Maintaining optimal wheel-rail adhesion is crucial for safe and efficient railway vehicle operation. Driving axles can experience torsional vibrations during operation, leading to compromised adhesion and potential axle damage. This paper presents a novel non-smooth model for analyzing these stick-slip vibrations in railway drive wheels and simulation results. The proposed model prioritizes simplicity while effectively capturing the essential friction characteristics for efficient dynamic simulations. By incorporating a set-valued friction law and formulating the equations of motion as a switch model, the model overcomes the limitations of traditional smooth models that struggle with stick-slip behavior due to stiffness in the equations. Numerical simulations demonstrate the model’s efficacy and efficiency compared to traditional approaches. The necessary integration steps in the stick phase prove to be a couple of times less relative to a physical model. This efficient and accurate model can be a valuable tool for developing control strategies to optimize wheel-rail adhesion and studying rail corrugation formation.