In the paper, an attempt to build solution of transient vibrations of railway track is presented. Excitations in this system generated by track structure, treated roughly as periodic ones, are often disturbed by track transient imperfections. Obtained solutions are based on Ritz-Galerkin method and then on Hermite’s polynomials application to the problem. Such a model doesn’t require a lot of computing and can be easily adapted e.g. for nonlinear track model. Our approach can take continuous foundation of Winkler or Pasternak layer type, or discrete rail support. For discrete not equi-spaced supports only finite number of them is considered. As the starting point for that solution, the response to Dirac’s impulse is employed. The method described in the paper is relatively efficient (beyond the resonances and near them) to analyse of infinite beams resting on continuous or discrete foundation, even with nonlinear characteristics.

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