This paper presents four approximation methods for the construction of safety related functions. These methods are: Enhanced Multivariate Adaptive Regression Splines, Stepwise Regression, Artificial Neural Network, and the Moving Least Square. The optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. Four benchmark problems used in crash and occupant simulation are employed to investigate the accuracy of the approximate or surrogate models. An occupant safety optimization problem is solved using these four response surfaces. Based on numerical results, a best, applicable approximation strategy for safety optimization is proposed in the end.