Measurements of the complex shear compliance (J*=J'-iJ'') of pure, polycrystalline lead, indium, and aluminum at closely spaced frequencies in the audio-frequency range have resulted in the discovery of multiple frequency dispersions of the resonance type. Values of the loss compliance (J'') are found to have sharply defined maxima in the range from 100 to 5000 cps; values of the storage compliance (J') rise to a maximum and then drop to pass through a minimum as a narrow (50 to 100 cps wide) dispersion region is traversed in the direction of increasing frequency. The shapes of the complex compliance vs frequency curves are thus similar to those found for the variation of the complex index of refraction with frequency (in absorption bands) at infrared and optical frequencies. The results indicate the presence of a dispersion mechanism different from those leading to the relaxation dispersions previously observed in connection with the mechanical properties of metals. Results on lead indicate that some of the resonances can be eliminated by high-temperature annealing of the sample material. The possibility that dislocation vibrations are responsible for the observed phenomena is considered, but no specific mechanism is found to explain the results. A number of dislocation theories are examined but these fail to predict any mechanical resonance dispersion at audio-frequencies. In addition to their theoretical implications, the results are believed to be of considerable practical importance since they indicate that certain materials when subject to mechanical vibrations of relatively low frequencies may undergo large changes in modulus at a particular frequency or frequencies.