Recent work in hydrocarbon reservoir monitoring has focused on developing coupled geomechanical/fluid-flow simulations to allow production-related geomechanical effects, such as compaction and subsidence, to be included in reservoir models. To predict realistic time-lapse seismic signatures, generation of appropriate elastic models from geomechanical output is required. These elastic models should include not only the fluid saturation effects of intrinsic, shape-induced, and stress-induced anisotropy, but also should incorporate nonlinear stress-dependent elasticity. To model nonlinear elasticity, we use a microstructural effective-medium approach in which elasticity is considered as a function of mineral stiffness and additional compliance is caused by the presence of low-aspect ratio displacement discontinuities. By jointly inverting observed ultrasonic P- and S-wave velocities to determine the distribution of such discontinuities, we assessed the appropriateness of modeling them as simple, planar, penny-shaped features. By using this approximation, we developed a simple analytical approach to predict how seismic velocities will vary with stress. We tested our approach by analyzing the elasticity of various sandstone samples; from a United Kingdom continental shelf (UKCS) reservoir, some of which display significant anisotropy, as well as two data sets taken from the literature.