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The method of optimal truncation is developed and applied to a variety of rotationally symmetric defects in elastic materials. Results are presented for oblate and prolate spheroidal voids, cracks, irregularly shaped voids, and compound inclusions. Most of the examples are in the frequency domain, but samples of time‐domain calculations are included. Physical interpretations of some features of the calculated amplitudes are given. Checks on accuracy of the results are emphasized and implemented.