Response surface method has won numerous concerns in the reliability analysis of structure due to its simplicity and practicability, especially quadratic response surface taking no account of cross terms is most widely used. However, for the complex ultimate state curved surface corresponding to strongly nonlinear, the approximate accuracy of quadratic response surface is apparently not enough, causing a biggish error in estimation of reliability. Although, theoretically, higher order response surface method can resolve this problem, the sharp increase of undetermined coefficient reduces calculation efficiency, and even, cannot achieve. Therefore, on the basis of univariate analysis of multivariable function, an algorithm which can reasonably determine higher order response surface form is presented in this article, able to effectively reduce the number of undetermined coefficients in response surface, so as to reduce computational difficulties and put forward improving measures for possible problems; In addition, based on the tactics of number-theoretic setpoint, a type of scheme of number-theoretic selecting point applicable to response surface method has been developed. Finally, through the analysis of examples, the suggested algorithm was validated, with the result showing that the algorithm has good accuracy and efficiency.