This study presents a novel approach for the viscoelastic (VE) modelling of railway track elements that depends on the combination of strong sides of classical and fractional derivative models (FDM) of viscoelasticity. First, parameters of a recent 10 parameter fractional derivative model are identified from dynamic mechanical analysis (DMA) data for three different elastomeric pads that are used in railway system. The FDM gives accurate results in wide frequency ranges, however, the time domain representation of this model includes fractional derivatives that substantially increase the computation time. To overcome this drawback, five-armed Generalized Maxwell Model (GMM) parameters are fitted in 0.01-1000 Hz to be used in the time domain analyses. The mathematical models of two distinct types of railway superstructure are obtained and solved by the Galerkin's method. The results of proposed framework are tested against measurements and the results of finite element model (FEM) analyses and very good agreement is observed.