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A technique for analyzing the problem of radiation from a point electromagnetic source located on a perfectly conducting cylinder of finite length is described. The method of attack is based on the spectral domain approach, generalized for the case of a curved surface with a large radius of curvature and used in conjunction with appropriate asymptotic theories. Special situations, such as radiation in the paraxial direction, or along caustics, are treated via modifications introduced in the conventional geometrical theory of diffraction (GTD) formulas. Some typical numerical results are presented.