Today many simulation routines concerning railway dynamics employ rather primitive contact models which are not necessarily suited for the specific wheel/rail contact problem. The objective of the present thesis is to derive a more flexible contact model which can be applied on a variety of contact problems. When it comes to the modelling of the wheel/rail contact it is always a compromise between computational speed and accuracy. Many numerical methods provide a very good accuracy, but since most railway simulations necessitates the evaluation of many consecutive contact situations the relative slow computational speed is extremely critical. To avoid this problem the present model is based on an analytical approach. The model derived in the thesis is a two-dimensional contact model based on elastic half spaces. It is demonstrated that the solution to a three-dimensional contact problem with no spin has many similarities with the two-dimensional solution. Thus, the results obtained with the present model can qualitatively be extended to the three-dimensional contact problem. The thesis is divided into two parts: one containing the derivation of the contact model and one containing examples of application. The model is applied on four different types of contact problems which cannot be treated with the most common contact models: - contact between corrugated surfaces - contact with velocity dependent friction coefficient - contact between rough surfaces - non-steady contact The calculations demonstrate with much clearness that the solution to the contact problem is very sensitive to the choice of contact model. This illustrates how crucial it is to employ an adequate contact model in a given simulation routine in order to obtain a realistic result. If the assumptions of the contact model do not fulfill the actual contact situation the result can be most erroneous and thus misleading.