In the past years, the safety of steel railway bridges has been questioned due to the coped beam connection sensitivity to fatigue and fatigue crack appearance. To ensure the safety of these railway bridges, the propagation of the fatigue crack needs to be analysed by performing regular inspection on the bridges. The frequency of these is required by the defined inspection intervals, which are based on the critical crack length and the number of loading cycles leading to this crack length. Laboratory tests and measurements on the bridges have been performed in the past to define inspection intervals, but had given only an approximation of the real situation. By creating a finite element model of a coped beam, a crack initiation and propagation analysis can be performed. This analysis provides an indication after how many loading cycles the crack will reach a critical length and guides towards revised inspection intervals. In this thesis, the objective is to take the first steps towards the revised inspection interval by performing a finite element analysis of the crack propagation of steel railway bridges. More specifically, this means an finite element analysis of the coped beam with extended finite element method. To achieve this goal, first, the location of the fatigue crack initiation has been investigated to understand where exactly in the cope the crack starts. This was performed by creating a local 3D linear elastic FE-model of the coped beam based on the boundary conditions, geometry, and loading from laboratory tests performed by Michael C.H. Yam and J.J. Roger Cheng. The the longitudinal stresses of the model were compared with stresses measured during the laboratory test to validate the crack initiation model. After the model was validated, the location of crack initiation was determined by identifying the location of the peak stresses. After completion of the crack initiation analysis, the crack propagation analysis can commence. For this, the FE-model was transformed from the crack initiation to the crack propagation model. In the same manner as with the crack initiation model, the propagation model has been based on the boundary conditions, geometry, and loading from the laboratory test. Since no path of the crack was registered during these laboratory tests, and thus could not be implemented in the model, a method for crack propagation analysis called extended finite element method (XFEM) has been used. The accuracy of this method has been confirmed by validating the stress intensity factor (SIF) values obtained for stationary cracks with three different mesh topologies and comparing the results with results from two established methods; J-integral and VCCT. After the validation of the crack propagation model, a sensitivity study was performed to understand the potential influence of modelling decisions on the number of load cycles versus crack length relation. With the mesh sensitivity analysis, a linear trend has been obtained for models with matching number of elements through the thickness. For the initial crack size sensitivity analysis, the effect of the number of elements through the thickness and the effect of mesh topology have been investigated. One element through the thickness and parallel mesh topology led to lower variation in the results. Additionally, a new value for the previously assumed Paris law coefficient C has been obtained by calibrating the number of cycles versus the crack length curve from FE-model to match the laboratory test results. In conclusion, this research provides recommendations for modelling crack propagation in a coped beam. The results are more reliable when keeping at least five finely meshed elements around the crack tip, using a parallel mesh topology, and using one element through the thickness. New value for the C coefficient from the Paris law has been suggested based on this research. The next step in this research is a continuation of the crack propagation model analysis to reduce the variation in the results. Furthermore, different loading positions and expansion from a simply supported beam model to a model with multiple spans should be analysed to bring us one step closer to the ultimate goal of redefining the inspection interval for coped beam steel bridges based on the models.