For non-ideal interpolation results of complex implicit nonlinear functions between non-normal distribution response and standard normal distribution inputs using stochastic response surface method, radial basis functions was used to replace Hermite polynomials so as to solve complex implicit nonlinear function interpolation problem for its excellent performance on scattered data interpolation. A few nonlinear analytical functions and uncertainty problems of the load carrying capacity of single circular concrete filled steel tubule (CFST) arch were used as examples to test and verify the precision of proposed method in non-normal distribution response interpolation and its engineering applicability. The results show that stochastic response surface method based on radial basis functions performs well in fitting highly nonlinear input implicit functions, and can achieve high precision on multi-parameters CFST arch load carrying capacity uncertainty problems. Meanwhile, the method has less sample points compared to the Hermite polynomials method.