Abstract: Based on the improved local piston theory, this paper presents the matrix expression of generalized aerodynamic forces expressed by the generalized coordinates. The results presented by this model agree well with those of solving unsteady Euler equations. This model greatly reduces the limitations of the classical piston theory on flight Mach number, airfoil thickness, and angle of attack. Though it is a linear model, the characteristic nonlinear behavior of the aeroelastic system under varying Mach number or angle of attack were also taken into consideration. Coupled with 2-DOF (two degrees of freedom) structural equations, supersonic or hypersonic aeroelasticity is analyzed in time domain and frequency domain. A series of 2D airfoil and 3D wing numerical examples were computed. Compared with the coupling unsteady Euler method or experimental data, this method ensures the high precision while improving the computational efficiency greatly.