Seismic technology has been used successfully to detect geomechanically induced signals in repeated seismic experiments from more than a dozen fields. To explain geomechanically induced time-lapse (4D) seismic signals, we use results from coupled reservoir and geomechanical modeling. The coupled simulation yields the 3D distribution, over time, of subsurface deformation and triaxial stress state in the reservoir and the surrounding rock. Predicted changes in triaxial stress state are then used to compute changes in anisotropic P- and S-wave velocities employing a stress sensitive rock-physics transform. We predict increasing vertical P-wave velocities inside the reservoir, accompanied by a negative change in P-wave anisotropy . Conversely, in the overburden and underburden, we have predicted a slowdown in vertical P-wave velocity and an increase in horizontal velocities. This corresponds to positive change in P-wave anisotropy . A stress sensitive rock-physics transform that predicts anisotropic velocity change from triaxial stress change offers an explanation for the apparent difference in stress sensitivity of P-wave velocity between the overburden and the reservoir. In a modeled example, the vertical velocity speedup per unit increase in vertical stress is more than twice as large in the overburden as in the reservoir. The difference is caused by the influence of the stress path K (i.e., the ratio between change in minimum horizontal effective stress and change in vertical effective stress ) on vertical velocity. The modeling suggests that time-lapse seismic technology has the potential to become a monitoring tool for stress path, a critical parameter in failure geomechanics.