Low-strain wave propagation velocity and attenuation are effective measures of state in particulate media. The standard resonant column test procedure is modified to facilitate the study of wave propagation at low strains. The system uses band-limited random noise excitation in combination with signal averaging to control the signal-to-noise ratio. This procedure is efficiently implemented by replacing typical peripheral devices with a signal analyzer and computer control. The methodology permits testing at very low strains (γ ≈ 10-8). The effect of non-linear system response on computed transfer functions is addressed. Other results include the analytical treatment of coupling between torsional and transverse modes, the evaluation of local low-strain shear parameters from solid specimens tested in torsion, and the use of multi-mode testing for the evaluation of field parameters.