The vibrational spectra of spherical samples of two granites, a diabase, an optical glass, and a ball bearing steel were observed in the frequency range 11-200 kHz. The frequencies were reduced to give mean velocities of compressional and shear waves, and the widths of resonance curves to give estimates of damping coefficients (Q). Close agreement with calculated frequencies for an isotropic homogeneous sphere is found for the glass, with rms deviations of the order of a few parts in 10,000 and a Q of about 6000, nearly independent of mode. For the diabase the rms deviation was about 3 parts per 1000, with a Q of about 1000; for Barre granite the rms deviation was 3 parts per 1000, with a Q of about 200; for Quincy granite the rms deviation was 14 parts per thousand, and Q was about 200. The steel ball showed an effect of hardening, with a decrease of velocity of a few parts per thousand as frequency increased from 30 to 200 kHz; Q was notably dependent on mode of vibration, about 8000-9000 for the torsional modes and most fundamental spheroidal modes but several times as high for the purely radial mode and several overtones. The observations of damping in the steel are roughly consistent with a simple theory in which all damping is attributed to shear, with a single, frequency-independent shear Q, whereas pure compression is undamped.