This paper presents a numerical method to construct transmitting boundaries for periodically supported railway tracks. This is realized by the derivation of impedance matrix for a half-infinite track. To achieve this, dynamic response of the infinite track corresponding to the half-infinite model is analyzed for a series of harmonic loading modes. The infinite problems are solved by virtue of Floquet transform. The developed method is applied to a periodically supported rail having a finite irregular zone subjected to harmonic loads. It is reduced to a dynamic problem of a finite track with the transmitting boundaries attached on both ends. Through comparison with the present method and a conventional way using a very long but finite railway model, the superiority over the truncated model is demonstrated.