The velocity dispersion in fused quartz and in Armco iron was investigated by measuring the resonant frequency of small cylinders using quartz crystals on the ends as drivers and detectors. With x‐cut crystals and y‐cut crystals the computed velocities of the dilatational waves in the range 2.0–5.0 Mc and shear waves in the range 1.5–3.0 Mc decrease with frequency. This decrease in both cases is regarded as unreasonably large and is ascribed primarily to sample geometry. Simple standing plane waves, either dilatational or shear, cannot satisfy the boundary conditions in a free cylinder. A mosaic crystal was then constructed of sectors of y‐cut crystals such that the driver generated and the detector transmitted only torsional waves. With these crystals and viscous coupling between the crystals and sample, the velocity in fused quartz was constant within ±1 m/s for the frequency range 0.6–3.0 Mc. The velocity in Armco iron was constant within ±2 m/s in the range 0.5–1.5 Mc and decreased about 10 m/s in the range 1.5–3.0 Mc.