A solution procedure is described for determing the twodimensional, two-degree-of-freedom flutter charateristics of arbitrary airfoils at large angles of attack. This procedure requires a simultaneous integration in time of the structural and fluid equations of motion. The fluid equations of motion are the unsteady conservative full potential equations, solved in a body-fitted moving coordinate system using an approximate factorization scheme. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. A wake cut behind a trailing edge is used to model the mathematical jump in potential, where the pressure is satisfied to be continuous by solving an approximate vorticity convection equation. The solid equations of motion are integrated in time using an 4th order Runge-Kutta method. Flutter is said to occur if small disturbances imposed on the airfoil attitude lead to divergent oscillatory motions at subsequent times.