Radiation from an axial magnetic line or slot source on the surface of a corrugated cylinder is considered. It is indicated that the power radiated in a given mode for the structure depends critically on the surface reactance and the circumference of the cylinder. In fact, for certain values of these parameters, particular modes are strongly excited and contain most of the radiated power. Numerical results are presented for several interesting cases.The analysis is extended to an elliptic cylinder whose surface also possesses an inductive reactance. In order to facilitate the solution it is necessary to assume a special azimuthal variation of the surface reactance. For the model as chosen, strong resonance characteristics are again obtained. This model may be adapted to study the problem of a corrugated panel on a flat metallic ground plane which is excited by a parallel slot source.