The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${ heta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.