The nonlinear behavior is approximated as a sequence of successively changing linear systems over a short time interval. Solution of nonlinear equations needs to iterative method such as Iterative algorithm. Iterative method attempts to solve a problem by finding successive approximations. The present study is concerned with methods of nonlinear static and dynamic analysis of structures, particularly for application to geometrically nonlinear space structures. The basis of the proposed method is a step-by-step procedure of parametric solution continuation using a predictor–corrector scheme. The prediction is made with help of some interpolation procedure. In this paper a simplex method of nonlinear dynamics response analysis is developed.