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The multibody simulation of railway dynamics needs a reliable and efficient method to properly describe the contact between wheel and rail. In this work innovative methods to evaluate the position of contact points are presented. The aim is to develop a method which can be implemented on-line, assuring a calculation time consistent with real-time calculations of multibody dynamics. At the same time it has to be very accurate, to properly predict the local forces at contact in order to describe even the wear of contact surfaces. In this work the authors present two different approaches to find stationary points during a multibody simulation. In the former the conditions to define a local minima are wrote in an analytical way. This makes possible to combine the conditions in order to reduce the analytic problem's dimension and then to solve numerically the problem with a low computational burden. The latter approach …