Sound penetration into large enclosures can be modeled approximately by ray methods. When these enclosures are elongated so as to admit simulation by a waveguide, the interplay between rays and guided modes becomes important. To clarify the relevant phenomenology, we examine the prototype problem of a rigid semi‐infinite baffled or unbaffled circular waveguide. Using the methodology of the geometrical theory of diffraction (GTD) and its modification to account for a guiding environment [L. B. Felsen and H. Y. Yee, J. Acoust. Soc. Am.44, 1028–1039 (1968)], the interior field for arbitrary plane wave incidence is constructed by edge diffracted‐multiple reflected ray tracing, by modal expansion, and by physical optics (PO) applied to the aperture field. Stationary phase evaluation of the PO modal excitation coefficients establishes the connection with GTD, especially the mechanism of coupling from GTD into the modal fields. By reciprocity, the radiation problem can be handled in a similar way. Some conclusions are drawn for guides with noncircular cross section. [Work supported by ONR.]