The block brake is an essential part of the brake system in freight wagons. During continuous braking or when other braking systems fail, the railway wheels endure extreme thermal and mechanical stresses through block braking. This thermomechanical load leads to plastic deformation, causing residual stresses and thermomechanical fatigue of the wheels. Because of the complex geometry and non-linear material behaviour, the respective calculations must be performed numerically. The aim of this master thesis is to develop suitable calculation models using the finite element software Abaqus that are able to accurately reproduce the stresses in the – with respect to fatigue – critical area of the wheel’s disk due to braking and the wheel-rail contact. Subsequently a fatigue strength assessment can be performed. The behaviour of the wheel material ER7 is described using a Chaboche model to reflect the cyclic plastic hardening and softening. The results suggest that cyclic plastic deformation causes noticeable damage at the inner and outer radii of the wheel disk. In contrast, the stresses in the disk from the wheel-rail contact, even at elevated temperatures, turn out to be low compared to the fatigue strength.