Abstract: A Green's function method for fully unsteady aerodynamics around three-dimensional bodies is outlined. This method can be used to evaluate the unsteady aerodynamic loads and derivatives of elastic aircraft. The equations of motion of an elastic aircraft are presented. And a unified method is employed to analyse the overall body motion stability and the flutter characteristics of an elastic aircraft. Numerical examples show that the results of the present method are in good agreement with the results of other methods.