Unsteady supersonic aerodynamic forces on an oscillating circular cylindrical shell are derived from the linearized equation of a potential flow on the basis of the assumption of circumferential wave number n ^> 1. The generalized aerodynamic forces calculated by the present aerodynamic theory are compared with those of the "exact" theory, the slenderbody theory, and the two-dimensional quasi-steady theory. The numerical results of the present theory are in good agreement with those of the "exact" theory except for small n. It is concluded from the qualitative argument that the slender-body theory may lead to an erroneous conclusion in flutter analysis, even though quantitative agreement between the generalized aerodynamic forces of the present and the slender-body theories is obtained. As for the two-dimensional quasi-steady theory, some doubts are clearly cast upon its applicability to the flutter analysis of a cylindrical shell except when the length-to-radius ratio and the reduced frequency are small enough compared with 1.