A finite element method to evaluate unsteady supersonic aerodynamic coefficients consistent with structural stiffness and inertia properties of a lifting surface is described. The grid and element system on the wing surface can be the same as in the structural analysis. Partial elements at wing and diaphragm edges are avoided, and downwash continuity is maintained, thereby yielding improved pressure distributions. Use of quadratic interpolation of velocity potentials and displacements improves accuracy, or leads to the necessity for fewer elements. Numerical results are obtained for several wing planforms at various Mach Numbers and reduced frequencies, and are compared with other methods.