The nonlinear behaviors of a plate under supersonic aerodynamic loads are investigated on the Approximate Inertial Manifolds (AIMs).The plate with infinite width is considered as a two-dimensional plane, and the aerodynamic loads are governed by the first order piston theory.Von Karman's large deformation plate theory is used to describe the system.Nonlinear Galerkin's method is applied to approaching the system, that is, the Approximate Inertial Manifolds is given and the goveming equation is projected onto the space spanned by the Eigen functions of the operator which are composed by the aero-elastic modes.