For the simulation of control surface buzz accurate prediction of the shock location and the chock strength is essential and this is currently achieved using Euler and RANS based CFD analysis. To calculate the motion of the control surface only the flap rotation mode needs to be modelled. In the current work the CFD solver is coupled with a modal based FEM solver. The multi-level hierarchical blending transformation methodology is applied for the aeroelastic analyses of complex geometries. The methodology is used for the treatment of blended control surfaces and the effect of the blending on the aero-structural response is measured. Forced clap oscillations of a Supersonic Transport (SST) configuration are simulated and the dynamic deformation of the wing and the unsteady pressure due to the forced oscillations are validated against experiments. Transonic buzz on a trailing edge flap is investigated on the Supersonic Transport configuration using the RANS and the Euler equations. Characteristics associated with buzz instability are reproduced computationally and the effect of the flap on the wing flutter is measured. Finally, aeroelastic simulations are performed on the Hawk aircraft. The combat flap configuration of the Hawk aircraft is investigated using CFD and the effect of the flap on wing flutter is assessed. The aeroelastic response of the rudder at supersonic freestream Mach numbers is studied. The importance of aerodynamic interference on the aeroelastic behaviour is assessed.