A numerical method for solving structural dynamic response was proposed by combining the theory of radial basis functions (RBFs) approximation and the collocation point methods. To solve the problem that using basic RBFs point interpolation method will bring great numerical oscillations, a multivariate interpolation function with the linear combination of each order differential terms was developed and the arithmetic steps were given. Unlike other numerical methods, there were no theoretical supposes about changing rules of acceleration and load within time interval, so this method had an applicability to solve jerk and jerk (third-order) equations. Actual examples showed that RBFs approximation method had simple computational process and improved the convergency and stability effectively.