When natural materials are loaded by a stress field, dramatic changes in modulus occur as the microstructure deforms, even if there is no permanent macroscopic damage. The effect is primarily due to pervasive, thin microfractures which easily close under load. The pressure derivative of a generalized elastic modulus, M=dC/dP, for most intact solids equals ~5, but can be two orders of magnitude higher for rocks and soils [1]. Nonlinear terms in the stress strain relation that governs material response can therefore be very important. Measurements of longitudinal and shear velocity under hydrostatic and uniaxial loading for various rocks are reported to illustrate these phenomena. Observations of amplitude dependent attenuation are presented to show direct evidence of nonlinear behavior. New results presented here for partially saturated rocks show the strongest nonlinear response yet reported.