A numerical approach is presented for computing unsteady aerodynamic effects on an airfoil that is undergoing independent pitching and/or plunging motion while attached to an accelerating body. The acceleration of the body may be at any angle to the horizontal axis. Grid speed terms are incorporated into a e rst-order e nite volume representation of the unsteady Euler equations, along with the appropriate acceleration terms for the boundary conditions. Unstructured grid methodology is utilized, along with a moving grid algorithm, to model the pitching/plunging of the airfoil within the grid. A NACA 0012 airfoil is considered for all work. Comparisons are made with nonaccelerating numerical and wind-tunnel data to demonstrate the validity of the methodology. Results are then presented for pitching and nonpitching airfoil, accelerated body cases to demonstrate the effects of the linear acceleration on the unsteady aerodynamics of the airfoil. The quantitative effect of the body acceleration on the aerodynamic coefe cients is seen to be a function of the type of motion (pitching/nonpitching ) imposed upon the airfoil.