Abstract Using Vlasov's general moment technical theory of elastic shells, the present paper derives the equations of equilibrium of a cylindrical shell with an arbitrary but slowly varying curvature of the cross-section. Supersonic flutter and divergence of one cylindrical shell with an elliptic cross-section are investigated numerically. The investigation is based on the linearized shallow-shell theory and on the aerodynamic piston theory. The shell is considered as a system with two (respectively with four) degrees of freedom. In a linear statement the stability region of the shell is determined by simultaneous action of both aerodynamic pressure and external axial load.