It is sure that the responses of practical structural dynamic systems considering parametric uncertainty under deterministic excitations also have characteristics of randomness. The acquisition of their statistical features is a difficult problem in vibration analysis of stochastic structural dynamic systems. Here, under the condition of a system’s uncertain characteristic parameters obeying Gauss distribution, based on Fourier-Hermite polynomial expansion, the stochastic responses of the dynamic system were solved using the generalized model dimension-reducing and the multi-dimensional Gauss-Hermite numerical quadrature to determine expansion coefficients, and obtain the system’s responses approximate solution in the form of explicit orthogonal polynomial function expansion. Then, the solution was embedded with the local Monte Carlo simulation (MCS) to form the statistical analysis method for random vibration systems, and acquire the statistical characteristics of the system responses. Furthermore, using FEM modeling, based on the proposed above method, the statistical analysis was conducted for plate structures’ vibration responses. Numerical simulation results showed that the statistical analysis results using the proposed method agree well with those using the direct MCS method to obtain statistical characteristics of random plate structures’ vibration responses; the statistical characteristics of random plate structures’ vibration responses under a continuous stiffness boundary condition can be predicted based on the FEM mesh refinement of a discrete stiffness boundary.