A straightforward numerical method for the computation of response of non-linear finite element system with uncertain parameters under stochastic loading is presented. This method is based on the special form of the probability destiny function of the random variables and, in particular, on the Gauss-Hermite integration rules to compute the response. In the method, a direct and simple formulation, which can just be signed as a symbol of function, is given to represent the relationships between random response and the randomness of the system parameters. In this way, it becomes much easier to obtain the response quantities by computing the double integrals, in which the stochastic parameter of the finite element system is considered as one of the integration variables in the computational procedure, as well as the external force with random characteristic. An example shows the performance of the method.