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The method expounded in the preceding paper is applied to the calculation of the scattering of elastic waves from axially symmetric voids and rigid obstacles. The eigenfunctions and surface tractions are presented in detail. Results are exhibited for direct and mode‐converted cross sections for a variety of scatterer shapes, including oblate and prolate spheroids with aspect ratios up to 7, pillboxes, and cones for ka varying from 0.1 to 10. Accuracy, computer time, and convergence properties are discussed.