Abstract: In order to study the environmental vibration response due to entering-station and leaving-station trains on their railway, a new dynamic periodic close form solution is introduced for the railway structure subjected to moving loads with variable speeds in this paper. Firstly, the general dynamical response in an elastic half space model subjected to the surface moving loads is obtained on the basis of Duhamel integral and dynamic reciprocity theorem. Secondly, in the case of a periodic railway track structure, the general dynamical response in the frequency domain is simplified in a form of summation within the track sleeper period instead of integral, which is obtained by transferring the moving loads on the rail to the moving of receiver backward within a periodic sleeper distance and the moving of loads within only one sleeper distance. The advantage of this formulation is that all of the dynamical analyses of the track system is carried out within a sleeper distance. In this way, the track response by the moving train can be obtained. Finally, by studying the cases of loads moving on the track structure with variable and constant speeds, the theory has been proved to be correct.