Detecting and Preventing wheels slipping is at the core of all researches related to railway vehicle dynamics. In this paper, three fast non-elliptic contact models are evaluated and compared to each other in terms of contact patch, pressure and traction distributions as well as the creep forces. Among them Johnson and Kalker method was really useful to the similar problems while the common assumption is elastic half-space that many errors could be made especially in gauge-corner contact. Based on the conclusions drawn from this evaluation, two new methods is proposed which results in more accurate contact patch and pressure distribution estimation while maintaining the same computational efficiency. The Beam and Bristle model are proposed for tire engineering in automotive industries but they can predict slip in wheel-rail contact too. New methods are typically used for tire engineering. Tire engineering usually is dealing with higher values of slippage than there is rail engineering. So that they can be applied into the saturation zone. At last a FEM analysis will be done for evaluating the methods proposed. Also in the special case there is similar experimental projects done by other scientists. It should be noted that good agreement between FEM analysis results, tire engineering models, experimental results has been found for several contact applications including S1002 wheel profile over UIC60 rail profile for four different initial braking speed 30, 60, 100, 140 km/h have been compared with experimental results.