The paper presents a numerical method for solving the aeroservoelastic problems. The method uses computational fluid dynamics and computational structural dynamics in a tightly-coupled manner to obtain time-accurate solutions of the generalized aeroelastic equations of motion. The transpiration method is applied to model the kinematic boundary conditions of moving surfaces in a Cartesian-grid based flow solver. The result is an efficient method for solving aeroelastic and aeroservoelastic problems even for very complex configurations. In this paper, numerical results for the verification of the developed method are presented. As a prelude to flutter-suppression control design using trailingedge flap, the effects of flap deflection on aeroelastic response of an experimental wing are studied. Preliminary results are presented in the paper.