Abstract: The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to study a new problem in mathematical physis:complex eigenvalue problem for a non-self-adjoint integro-differential equation(4-th order) of Yolterra's type.Exact solution for the aeroelastic system is obtained In contrast to various approximate analysis,our resulting critical curve agrees satisfactorily with experimental data, free from divergence in low supersonic region.Moreover, we observe some notable physical behaviors;(1)mutual separation between flutter and vacuum frequency spectrum,(2) degeneracy of critical Mach number.The present method may be generalized in solving the supersonic flutter problems for 3-din ensiunal airfoil models as well as blade cascade in turbo-generator.