A model for the prediction of the initiation and growth of roughness on the rail is presented. The vertical interaction between a train and the track is calculated as a time history for single or multiple wheels moving on periodically supported rails, using a wavenumber-based approach. This vertical dynamic wheel/rail force arises from the varying stiffness due to discrete supports (i.e. parametric excitation) and the roughness excitation on the railhead. The tangential contact problem between the wheel and rail is modelled using an unsteady two-dimensional approach and also using the three-dimensional contact model, FASTSIM. This enables the slip and stick regions in the contact patch to be identified from the input geometry and creepage between the wheel and rail. The long-term wear growth is then predicted by applying repeated passages of the vehicle wheelsets, as part of an iterative solution.