The transonic aeroelastic analyses have been performed for a Rap of airfoil. The Euler equations are solved using a finite volume scheme for the aerodynamic calculation. The dynamic grids are generated by a spring analogy method. The unsteady aerodynamic loads are calculated in the time domain and transformed in the frequency domain using a transient pulse technique. The time responses of aeroelastic system are obtained by integrating the structural equations of motion and the unsteady aerodynamic forces using the fourth order Runge-Kutta time stepping method. The aerodynamic loads of airfoils with a flap for the steady and unsteady flow are validated by comparing the present results with the existing experimental data. The aeroelastic time responses for a flapped airfoil are computed for various initial flap angles, structural damping coefficients and Mach numbers. The effects of the stiffness of the flap hinge spring and the initial flap angle on the flutter are also investigated in the transonic speeds. Copyright (C) 1996 Elsevier Science Ltd.