Mechanical hysteresis loops have been obtained for various polycrystalline solids in a manner similar to that used for magnetic materials. Half-wavelength samples are driven mechanically at a frequency of 14 000 cps producing stresses at the center of the sample of 40 000 lb/in2. Stress is measured using transverse ultrasonic waves in a technique similar to that of photoelasticity. Strain is measured for the same portion of the bar, and the resulting information is displayed on an oscilloscope. A description of the fundamental techniques is given. The results are compared to analytical predictions of the behavior of vibrating mechanical systems. (This work is supported by the Office of Naval Research.)