This paper discusses modelling of floating-slab tracks on rigid foundations. The model consists of an upper Euler–Bernoulli beam to account for both the rails and a lower Euler–Bernoulli beam to account for the slab. There are two continuous resilient layers in the model: one to account for railpads between the rails and the slab and one to account for slab-bearings underneath the slab. The Fourier transformation method is used to calculate displacements of such a track under an oscillating moving load. These results are used to calculate the cut-on frequencies and critical velocity of the track. The work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves, critical velocities, load-velocity lines and coupling of systems in the wavenumber-frequency domain. The paper offers a complete treatment of the issues important to the analysis of a double-beam system not elsewhere available in the published literature.