Poorly consolidated rock around the wellbore may become unstable after the process of well shut-down and restart. Possible reasons for instability include pressure recovery and water hammer effects. These are defined and analyzed by two different fluid mechanics models. The pressure recovery model results in a quasi-static solution defined in the context of Darcy theory. The water hammer model is based on inertial effects inside the wellbore, and seeks to specify the magnitude of short-term stress variation from the generation of a compressional shockwave due to sudden shut-down of a flowing well. To quantify the effect of well shut-down on rock stability, a fully coupled geomechanics model accounting for the changes of fluid pressure is developed. The redistribution of fluid pressure in a reservoir are analytically solved and coupled with the stress model, while the water hammer equations provide a boundary condition for the bottom-hole pressure. This approach allows a direct solution for the relationships among fluid properties, rock properties, and production parameters, within the context of rock stability, and defined as an effective stress-dependent strength or yield threshold. Model calculations demonstrate that the fluctuations of effective stresses and shear stresses may reach several hundred kPa because of the pressure wave created by a water hammer inside the wellbore. The model can be applied to evaluate the risks of triggering rock instability and select the wells that may start sanding if they are shut-down or started up abruptly. Furthermore, the paper provides a method to quantify the effect of pressure fluctuation on rock stability.