Abstract: Combined with a generalized Symplectic method and a periodical pseudo-steady method and a pseudo-excitation method for random vibration, a general Symplectic model for the random vibration of a time-variant vehicle-track coupled system was established. This model was used to calculate the influence of the frequency-dependent stiffness of rail pads on the frequency-domain random vibration of a time-variant vehicle-track coupled system, which was further compared with the frequency-domain random vibration of a time-invariant vehicle-track coupled system. The conclusions show that:as for the low-speed subway, the difference of the vertical frequency-domain random vibrations of both vehicle wheels and the structures under vehicle wheels between in time-variant vehicle-track coupled model and in time-invariant one is small within the variable range of the low-frequency initial stiffness and the frequency-dependent stiffness of existing rail pads. Therefore, the time-invariant vehicle-track coupled model can meet the engineering requirement in subway. In high-speed railway, the greater is the frequency-dependent extent of the stiffness of rail pads, the bigger is the disparity of the highest power peaks and the corresponding dominant frequencies of both vehicle wheels and the structures under vehicle wheels between in time-variant model and in time-invariant one; thus, the time-variant vehicle-track coupled model other than the time-invariant one should be applied for the accurate calculation of the random vibrations of high-speed railway with the highly frequency-dependent stiffness of rail pads.