Abstract: The 2 D Reynolds averaged compressible unsteady full Navier Stokes equations are solved by using the Beam Warming scheme with Baldwin Lomax turbulent model about the flexible wall airfoil.A method is proposed which can treat the locally changing surface of airfoils.The adaptive surface in the shock region can influence the shock/boundary layer interaction.Comparison has been made between the flow fields over NACA0021 airfoil with and without the flexible wall.Since we use the time marching method to get the steady results,the main difficulty in the present case is the treatment of the flexible wall boundary which changes its shape as the solution proceeds.The deflections of the flexible wall as function of the pressure over it can be found by the mechanics of the material.We proposed a method of locally changing grids to avoid the global interpolation.The locally changed grids maintain the good quality of the original grids.The calculated results show that a strong shock splits into two weak shocks in comparison with the case without the control.