Static determinations of hysteresis of typical shaft materials in torsion show that the values are low for high-quality materials in unidirectional loading after several cycles of loading up to a shear-stress amplitude of 24,000 psi. For reversed loading, the hysteresis becomes several times larger and may be of significance in accurate torque-weighing devices. The measured hysteresis in a tubular specimen had values 3 to 4 times that for a solid specimen. Two nonmagnetic materials displayed very low values of hysteresis. The apparatus developed for this investigation had sensitivity sufficient to measure displacement changes of 0.002 per cent of the full-load deflection, and was designed to eliminate errors due to temperature changes, extraneous loads, and external vibration.