Rail is a component of rail track playing crucial role in the dynamics and railways safety analysis due to its direct contact with vehicles wheels. Therefore the dynamic behaviour prediction of rails is essential in terms of simulation assisted predictive maintenance. Analytical solutions are benchmarks for other approaches and can be supportive for data analysis related to measurements and history based holistic investigations. In addition, analytical models, when validated, are good extensions for case study of potential situations that are difficult to approach with diagnostic tools. Obviously, they are also helpful in the improvements of existing structures at the stage of prototypes design and their testing before industrial implementation. The strongest dynamic response of rail track can be recognized in vertical vibrations. In this case, several models are being used depending of their level of complexity and possibility to analyse more detailed behaviour. The determination of which models are the best in terms of their accuracy and the range of applicability is still an open problem. This paper aims at study of 3 different models of rail track describing vertical vibrations of rails: one-layer, two-layer and relatively new “beam-inside-beam” model developed for the “head on web” problem description. The models are formulated and analysed in terms of their matching in the case of parameters taken from realistic structures and vehicles.