The acoustic field of a plane wave incident on an elastic cylinder may be decomposed into two parts, one representing circumferential waves that propagate around the cylinder, the other part obeying in the high‐frequency limit the laws of geometrical optics. The latter part is studied in this paper, and is decomposed into the specularly reflected wave and into a series of transmitted waves which traverse the cylinder either directly along a secant, or undergo additional internal reflections with and without mode convention (compressional to shear type, orvice versa). Wavefront loci and amplitudes of these waves are calculated using the saddle‐point method, and the corresponding reflection and transmission coefficients are shown to reduce, for the case of a large cylinder, to the known expressions for a flat elastic half‐space in contact with a liquid.