This paper features a method to synthesize the track irregularities, by which the alignment may be analytically represented by a pseudo-stochastic function, as well as the implementation of such method in the numerical simulation of the dynamic behaviour of the railway vehicles. The method thus suggested allows a convenient formulation of the limits of the interval specific to the wavelengths of the track lateral irregularities, so that it will be representative for the frequency range of the vehicle lateral vibrations. The Part I of this paper demonstrates the method to synthesize the track alignment and its basic elements – the power spectral density of the track irregularities, as per ORE B176 and the values associated with the track quality levels, mentioned in the UIC 518 Leaflet. The Part II introduces the results of the numerical simulations regarding the dynamic behaviour of the railway vehicle during the circulation on a tangent track with lateral irregularities, synthesized as in the method herein.