The grid fin is an unconventional control surface used on missiles and rockets. Although aerodynamics of grid fin has been studied by many researchers, few considers the aeroelastic effects. In this paper, the static aeroelastic simulations are performed by the coupled viscous computational fluid dynamics with structural flexibility method in transonic and supersonic regimes. The developed coupling strategy including fluid-structure interpolation and volume mesh motion schemes is based on radial basis functions. Results are presented for a vertical and a horizontal grid fin mounted on a body. Horizontal fin results show that the deformed fin is swept backward and the axial force is increased. The deformations also induce the movement of center of pressure, causing the reduction and reversal in hinge moment for the transonic flow and the supersonic flow, respectively. For the vertical fin, the local effective incidences are increased due to the deformations so that the deformed normal force is greater than the original one. At high angles of attack, both the deformed and original normal forces experience a sudden reduction due to the interference of leeward separated vortices on the fin. Additionally, the increment in axial force is shown to correlate strongly with the increment in the square of normal force. (C) 2017 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd.