The dissipation in an elastic medium is represented by a dissipation mechanism which is similar to one used in an earlier paper [M. Caputo, Geophys. J. R. Astron. Soc. 13, 529–539 (1967)], but is simpler and has a frequency‐independentQ−1. The vibrations of a plate are studied by obtaining the eigenfrequencies, the amplitude of the displacement, the dispersion relation, theQ−1, the hysteresis cycle, and the yield stress.Subject Classification: [43]40.24.