The thesis deals with the computation of the crack driving force for already existing cracks loaded by the contact between a wheel and a rail. The main focus is related to the influence of loading parameters. These are the normal load causing a contact pressure and the slip causing a surface traction on the rail surface. A main effort is laid on the investigation of the effect of the plastic deformation on the computed crack driving force. Further investigations are concerning the effect of the friction coefficient between the crack faces and the friction between wheel and the rail on the computed crack driving force. The influence of numerical parameters of the model such as boundary conditions, mesh size and mesh distribution on the results is critically reviewed. The configurational force concept has been chosen for the calculation of the crack driving force as new available method for finite element (FE) programs which offers the basic features needed to handle cracks in a cyclically plastified environment. All investigations on cracks have been carried out using a two-dimensional finite element model. The first chapter explains the scope of the thesis. The fracture mechanics approaches are discussed in chapter two. Subsequently, the configurational force concept is chosen as the crack driving force used in the thesis. A two-dimensional FE contact-crack model is introduced in chapters three and four. The fifth chapter includes a numerical examination of the chosen FE model variables and their effect on the computed crack driving force. The sixth chapter summarises the results. The seventh chapter consists of published scientific papers and an unpublished experimental verification of the computed results.