The aim is the determination of the dynamic response of the guideway to the action of a travelling disturbance source. The structure is modelled as a continuous Bernoulli-Euler beam which is made a periodic system by the attachment of equally spaced supports. The steady-state response is obtained in the form of a superposition of travelling waves. Also the problem of free wave propagation is briefly discussed. The method is based on Floquet’s theorem and consists in a direct solution of the differential equation for the continuous beam, which allows to determine the displacement field in any cell of the periodic system.