Abstract: The Symplectic mathematics model of random vibration for a vehicle-track coupled system was established with Pseudo Excitation Method (PEM) and Symplectic Mathematics of infinitely periodic sub-structures. The model was used to explore the influence of the frequency-dependent stiffness of rail pads on the random vibration of a vehicle-track coupled system. The conclusions show that: the frequency-dependent stiffness of rail pads has little effect on the vertical random vibration of a vehicle body, yet alters the middle- and high-frequency vertical random vibration amplitudes of a vehicle bogie, and meanwhile significantly increases the power peak and the 1st dominant frequency of the vertical random vibration of both vehicle wheelset and steel rail; the variation of the power peak and the 1st dominant frequency of wheelset' vertical random vibration with the low-frequency initial stiffness of rail pads or the frequency-dependent extent of their stiffness appears the wavy gradual and the stepped increasing trend, respectively; In the stiffness scope of the commonly-used rail pads, the power peak of wheelset' vertical random vibration has the maximal increase of 17.5 times, and its 1st dominant frequency also has the biggest increment of 40 Hz. Thus, in order to accurately predict the frequency-domain characteristics of the random vibration of a vehicle bogie, of wheels and of the fundamental structure under wheels, it is necessary to comprehensively consider the low-frequency initial stiffness of rail pads and the variation of their stiffness with frequencies.