Radial basis functions are widely used in the shape function construction during the function fitting process of Response Surface Method (RSM) However, the shape parameters of radial basis functions significantly influence the condition number of the moment matrix and the accuracy of the interpolation result. This paper presents a study on the selection of the shape parameters of the most frequently-used Multiquadric (MQ) and Gaussian (GS) radial basis functions and also MQ and GS radial basis functions coupled with linear polynomial function for the nonlinear contact-impact problems. The whole vehicle impact case is considered and the surrogate model technique of RSM is used to establish the objective and constrained functions. Finally, the values of shape parameters are obtained for the nonlinear dynamic mechanical system.