For accurate measurements of stress-strain hysteresis loops at strains below 10(-3)%, a torsional motion monitoring system was modified to incorporate micro-proximitors. A micro-proximitor system with enlarged target arms resulted in about 50 times higher resolution in motion monitoring than previously possible. The four proximitor signals (instead of two) were measured, compared, and averaged to insure that pure torsion of the system was generated and that any bending did not-enter the measurement. Ambient noise was controlled by using a low-pass filter and/or a vibration isolation table. With this new system, shear modulus was measured at strains as low as 2 . 10(-5)%, and hysteretic damping was measured at strains as low as 6 . 10(-5)%. Below the elastic threshold strain, shear modulus of dry sand measured in the cyclic torsional shear test is independent of strain amplitude. Hysteretic damping exists below the elastic threshold and is independent of strain amplitude, even though the value is quite small.