A finite element approach is developed to analyze the panel flutter problems of thin plate-like composite panels with patched cracks. The panel studied is a compound structure that comprises three layers including a thin cracked panel, an adhesive, and a thin patch. A 48-degree-of-freedom (DOF) triangular crack patching element is derived for numerically analyzing the compound structure. The aerodynamic pressure acting on the panel is estimated using linearized piston theory with aerodynamic damping effect neglected. By a proper tailoring of the materials, very high flutter and/or divergence boundary could usually be obtained for the composite panels. The existence of a crack usually reduces the aeroelastic stability boundary; however, some exceptions were found for the composite panel within certain range of specific filament orientation. The deterioration in flutter/divergence performance due to a crack can, in general, be cured by means of patching, and anisotropic patching is more effective as compared to the isotropic patching provided that the tailoring of the structural parameters is done correctly.