The periodically supported beam is an analytical model of the dynamics of a railway track, where each rail together with its supports (sleepers) is independent of the other one. However , the sleepers connect the two rails and their behaviour could influence the response. This study develops an analytical model for this type of track by considering the sleepers as Euler-Bernoulli beams resting on a visco-elastic foundation. By using a relation between the reaction forces and displacement of the periodically supported beam [1], we can obtain a dynamic equation of a sleeper based on Dirac delta distribution. Then, the response of the sleepers can be obtained by using the Green function. This model is a fast method to calculate the dynamic responses of railway sleepers and track.