Abstract: The vertical coupling model of vehicle-track systems isset up in the case of the track as an infinite periodic structure. Therandom irregularity excitation of the rail is transformed into adeterministic harmonic excitation with the pseudo excitation method, and thefrequency response of the track and the power spectrum density (PSD) of thesystem response are analyzed using the symplectic algorithm. In addition,there are only 26 DOFs in the computational model to have an efficient andaccurate solution. The model is verified with the conventional FEM, and theinfluence of the vehicle velocity on the system vibration is investigated.