A generalized mode-matching method is developed to study the scattering properties of conducting cylinders with periodic grooves of arbitrary cross section. Reflection matrices are derived to reduce the number of unknowns. This method is illustrated by studying three types of periodic grooves with dielectric filling on a cylindrical surface. Radar cross sections by an incident TE wave are obtained, and the effects of frequency, groove profile, groove depth, and filling permittivity are analyzed.¿ 1997 American Geophysical Union