Developments of modern rail transportation require advanced methods for analysing dynamics of a railway track as an infinitely long periodic structure. A Fourier transform-based method has been formulated for calculating the response of a conventional ballasted railway track subject to a moving harmonic load. The method is then extended to account for the track complicated by rail dampers installed between sleepers. Equations derived so far require that all the supports and attachments to the rail are coupled through the rail only. This, however, is not the case for non-ballasted slab tracks such as those used in China for high-speed and underground trains. For those tracks, in addition to the rail, fastener systems within a slab are also coupled by the slab. Therefore, the Fourier transform-based method must be further extended to give revised equations which, in consideration of noise evaluation, should be also appropriate for sound radiation prediction. This is the first task of this paper. The second task of this paper is to propose an appropriate procedure for predicting sound radiations from the track using the 2.5D acoustical boundary element method. The revised equations are then used to investigate the dynamics of a typical high-speed railway track, including dispersion curves of the track, responses of the rail and slab to a moving harmonic load, and vibration decay rate along the rail. And finally, sound radiations from this track are briefly examined using the proposed procedure.