Abstract: A new random vibration-based assessment method for coupled vehicle-track system with uncertain parameters subjected to random track irregularity is proposed in this paper. The vehicle system is simplified as a spring-mass-damper system model by using physical coordinates, and the uncertainties in the primary suspension and secondary suspension for the body, bogies and wheels are modeled by Gaussian random variables. The track is treated as a Bernoulli-Euler beam connected to sleepers and the ballast and is regarded as an infinite periodic structure. The state equation for a typical sub-structure of the track is established in the Hamiltonian system. The dynamic equations of the coupled vehicle-track system under the mixed physical coordinates and symplectic dual coordinates are established based on the wheel-rail coupling relations. The control equation with respect to the uncertain parameters is derived by using the Hermitian orthogonal polynomials for dynamic analysis of the coupled systems. By using the periodic features of the track, the "curse of dimensionality" of the control equation is effectively reduced. The wheel-rail contact forces due to the track irregularity are assumed to be fully coherent stationary random processes. An assessment of the random vibration with respect to the uncertain parameters is established for the coupled vehicle-track system by using the pseudo-excitation method (PEM). The proposed method is compared with the Monte Carlo simulations, and it is found that good agreements are achieved even for cases with strong uncertainties in system parameters.