Abstract: A numerical method is presented to calculate unsteady aerodynamics with Euler equations. Different from the traditional method in which unsteady flow field is calculated by recreating or deforming meshes at each time-step, dynamic approximate boundary conditions are satisfied on the stationary inner boundary so that only one set of mesh is needed in the present numerical method. A series of unsteady cases are calculated by this method, the results of which are compared with Euler solutions with accurate boundary conditions on moving meshes and experimental data. The relative errors due to the variation of pitching angles of the airfoil and Mach number are analyzed quantitatively. The CFD solver with the dynamic approximate boundary conditions is coupled with structural equations to predict the aeroelastic problem of an airfoil. A standard computing model of aeroelasticity (2-D Isogai wing with S type flutter boundary) is analyzed. The computed flutter boundaries agree well with the results of accurate boundary conditions. It is shown that the Euler equations based on dynamic approximate boundary conditions are brief and efficient, and are adequate to represent the airfoils with small deformation in unsteady cases and can be used for aeroelastic analysis.