A panel type mean lifting surface method has been developed for the computation of unsteady pressure distributions on harmonically oscillating wings in compressible, subsonic flow. The velocity potential function has been used as the prime unknown in the formulation. Good agreement is observed between this theory and experiments for finite wings with and without control surfaces in steady and unsteady flow. A novel acceleration potential function based panel method has also been developed which exhibits a simple Kernel function. Limited testing of this method shows good agreement with experiments. This method can perform the desired calculations at approximately four times the speed of the velocity potential formulation. Both methods may be readily extended to include thickness and interference effects.