Friction is a phenomenon involving elastic interactions, plastic deformation and failure processes at different length scales. The friction coefficient is one of the most relevant parameters for the rolling contact of railway wheels and rails. A model of dry friction is established based on the method of movable cellular automata (MCA). The influence of pressure and sliding velocity has been investigated by means of a large number of numerical simulations. A general qualitative conclusion is the fact that dynamic processes of plastic deformation and fracture at the nanolevel are of great importance. Within this model, the contact temperature can also be considered by its influence on the strength of materials. The new friction law is applied to the calculation of stresses, deformations and tractive forces in wheel/rail contact with rough surfaces. Thus, the understanding for the physical background of dry friction in engineering applications can be considerably improved. (c) 2006 Elsevier B.V. All rights reserved.