In this paper the dynamics of railway tracks on non-uniform viscoelastic foundations are investigated using a new analytical model. Firstly, a model is developed for a beam where the behaviour of supports are changed periodically along the length of the beam. By using a periodicity condition, the dynamic equation of the Euler-Bernoulli beam leads to a general relation between the reaction forces of the supports and the displacement of the beam. Then, the responses are computed by combining this relation and the constitutive law for the supports. Thereafter, a periodically supported beam on a non-uniform foundation is considered with a support system including a defect zone where the the behaviour of the supports is different from the non-defect supports. Then, a larger interval of the support system bounding this defect zone is considered as one period of a periodical support system provided that dynamic responses outside this zone are unchanged and equal to the steady responses. The analytical method is efficient when the number of the supports in one period is not very large. Otherwise, a numerical method has been developed to compute the response by using the fast Fourier transforms and an iteration procedure. This method is simple and fast, particularly when using the fast Fourier transform, to compute the dynamic responses of railway tracks on non-uniform foundations.