The demand to investigate and predict the surface deterioration phenomena in the wheel-rail interface necessitates fast and accurate contact modelling. During the past 20 years, there have been attempts to determine more realistic contact patch and stress distributions using fast simplified methods. The main aim of the present work is to compare some of these state-of-the-art, non-elliptic contact models available in the literature. This is considered as the first step to develop a fast and accurate non-elliptic contact model that can be used on-line with vehicle dynamics analysis. Three contact models, namely STRIPES, Kik-Piotrowski and Linder are implemented and compared in terms of contact patch prediction, as well as contact pressure and traction distributions. The evaluation of these models using CONTACT software indicate the need for improvement of contact patch and pressure estimation in certain contact cases.