A state-dependent method to model contact nonlinearities in rolling contacts is proposed. By pre-calculation of contact stiffness and contact filters as functions of vertical relative displacement, a computationally efficient modelling approach based on a moving point force description is developed. Simulations using the state-dependent model have been analysed by comparison with measurements. Results from the investigated case – consisting of a steel ball rolling over a steel beam having two different degrees of roughness – show good agreement between nonlinear simulations and measured beam vibrations. The promising results obtained with the proposed method are potentially applicable to wheel–rail interaction and rolling element bearings.