The equations governing the propagation of longitudinal and of torsional waves in thin, tapered rods are of similar form. It is, therefore, possible to use the method by which longitudinally resonant amplitude transformers were previously designed [J. Acoust. Soc. Am.35, 1367–1378, (1963)] to design torsionally resonant transformers. These torsional transformers are capable of extremely high magnifications.