The problem investigated in this paper comes from railway engineering. It is known that geometrical irregularities of the rail head rolling surface produce additional force when the train runs on track. This force can be quite significant and should not be neglected in the analysis, especially when one deals with high-speed railways. In this paper, an analytical method of modelling of such irregularities is presented. The detailed description of this method is associated with its practical application to the analysis of the rail track dynamic response to moving train. However, stochastic analysis of the presented model is omitted in this paper and left for further work. This should include a number of realisations along with statistical analysis of results, or description of the rail track subjected to moving train in terms of stochastic differential equations, which is the main direction of the authors future investigations.
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