The utility of laser-induced phonon spectroscopy in the determination of the elastic constants of small single crystals is demonstrated in the case of olivine of Fo89 composition. Experimental precision in the acoustic velocities is approximately 0.2%. The elastic constants derived in the current experiments have formal uncertainties of less than 1%. In analysis of all olivine data with compositions between Fo0 and Fo100, diagonal elastic constants are linear in composition to better than 1%, while off-diagonal constants exhibit scatter of several percent. Preliminary data at high pressure indicate that this technique can be applied to studies of mineral elasticity under extreme conditions. ¿ American Geophysical Union 1989