The response surface method (RSM), which is characterized by its understandability and efficiency, has been widely applied to reliability with implicit performance function. Nevertheless, due to multiple failure modes, it is difficult to apply the RSM directly to system reliability analysis. Further, because of the existence of multiple design points, the design point based RSM is unfeasible for system reliability. On this basis, this paper apply a RSM for classical system reliability by combining the complete system failure process with the high order response surface method. Firstly, following the idea of complete system failure process, a single equivalent performance function for system reliability is derived. Hence the application of RSM can possibly be applied. Secondly, by introducing high order modification, the stochastic response surface method is used to fit the equivalent performance function. In this way, the introduction of design points iteration is avoided. Thirdly, Monte Carlo method is adopted to evaluate the failure probability of the response surface function. Finally, several examples are investigated to verify the accuracy and efficiency of the method.