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A pulsatile flow of micropolar fluid through an elastic vessel with small displacement has been developed to model the blood flow in arteries. For numerical solution of governing equations, the finite difference method has been utilized. Also, by choosing the suitable boundary conditions and using the solution procedures of fluid structure interaction (FSI) problems, the fluid flow simulation has been used in different states, such as rigid or flexible wall and classical or Cosserat theories. We show that our solution in this study is in good agreeable with experimental and analytical results. This article presents the best modeling for blood flow simulation in biomedical jobs with doing stability analysis for numerical code of micropolar fluid flow model and choosing a suitable relaxation factor for receiving to convergence solution.