In this paper, the supersonic flutter characteristics of doubly curved sandwich shell panels, viz., cylindrical and spherical shells, with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible shell element developed based on higher-order structural theory. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacement at the interface. The strain-displacement relation is accurately introduced in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange's equation of motion, are obtained by QR algorithm. The accuracy of the present formulation is validated considering the problems for which solutions are available in the literature. A detailed numerical study is conducted to highlight the significance of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the shell thickness and the aspect ratio, radius-to-thickness ratio, and temperature on the flutter boundaries. © 2015 Elsevier Ltd.