In this paper, we present a method for solving coupled problem. This method is mainly based on the successive approximations method. The external force acting on the structure is replaced by λ = p (x1, H + u (x1, λ)). Then we have a nonlinear equation of unknown λ to solve by successive approximations method. By this method, we obtain easily the analytic expression of the displacement. In addition, good results are obtained with only a few iterations.
 Quateroni, A., Tuveri, M. and Veneziani, A. (2000) Computational Vascular Fluid Dynamics, Problem Models and Methods. Computing and Visualization in Science, 2, 163-197.
 Blouza, A., Dumas, L. and Mbaye, I. (2008) Multiobjective Optimization of a Stent in a Fluid-Structure Context. Proceedings of Genetic and Evolutionary Computation Conference (GECCO), 2056-2060.
 Mbaye, I. (2012) Controllability Approach for a Fluid-Structure Interaction Problem. Applied Mathematics, 3, 213-216.
 Murea, C. (2005) The BFGS Algorithm for Nonlinear Least Squares Problem Arising from Blood Flow in Arteries. Computers Mathematics with Applications, 49, 171-186.
 Hecht, F. and Pironneau, O. (2003) A Finite Element Software for PDE FreeFem++.