We have used Mason and Bateman's formulation of the Akhiezer mechanism to compute the ultrasonic attenuation in quartz. The results are compared with the experimental measurements of various workers. For the seven pure‐mode ultrasonic waves that propagate on thex, y, andzaxes in quartz the agreement between the calculated and measured attenuation coefficients is always to better than a factor of 2. This is the first extensive calculation of its kind on a trigonal crystal, and it is particularly gratifying that the theory explains the approximate equality of the attenuations of longitudinal and transverse waves. We have also performed similar calculations on fused silica, but in this case the measured attenuation exceeds the Akhiezer attenuation by more than an order of magnitude. It appears that some other relaxation mechanism dominates the attenuation in this material.