Conventional descriptions of the stress dependence of acoustic velocities in rock are often based on microcrack models. A more general, model-independent description that ignores microstructure is third-order elasticity theory. This theory has had much success in metals and crystals, and has recently been applied to rocks as well. We measured third-order elastic constants in several rocks both dry and water saturated. A five-velocity-measurement technique was used where a rock sample is stressed either hydrostatically or uniaxially, and compressional and shear velocities are measured as functions of stress. In dry rocks we find that third-order elasticity theory provides a good description of velocity versus stress. However, in water-saturated rocks, agreement between theoretical predictions and measurements is significantly worse than in dry rocks. This indicates that third-order elasticity theory does not fully describe the stress dependence of velocities in water-saturated rock under our experimental conditions. Detailed analysis of the velocity data suggests that rock dilatancy may be responsible for the discrepancies between theory and experiment.