Inertial manifolds with delay (IMD) are applied to the numerical analysis for two-dimensional and three-dimensional panel flutter problems in order to demonstrate their high efficiency in continuous dynamic systems or systems with infinite dimensions. First, Von Kármán's large deformation theory and the first-order piston theory are used to model the system, and a set of nonlinear partial differential equations is obtained. Then, the nonlinear Galerkin method based on IMD is introduced to approach the original infinite dimensional dynamic system, and some expressions with time delay are proposed to reveal the interactions between the higher modes and lower modes. As a result, the degrees-of-freedom of the system are reduced, and computing time can be saved remarkably. Finally, the dynamic behaviors of the system are simulated numerically to make a detailed comparison between IMD and the traditional Galerkin method (TGM). Finally, a conclusion can be drawn that IMD could reduce the computation time up to 7–50%, keeping the same accuracy, and thus its high efficiency is proved. Moreover, the method presented can be extended and applied to other dissipative dynamic systems with large degrees-of-freedom.