Geomechanics is the science of how rocks deform, sometimes to failure, due to changes in stress, temperature, and other environmental processes. Pore pressure is also very important, as it plays a significant role in these processes. Geopressure plays an important role in all aspects of geomechanics. Changes in pore pressure alter the state of effective stress acting on the subsurface formations. Increase in effective stress can cause failure by compaction or shearing. Therefore, the ability to model the stresses and their responses to different pore pressure scenarios is of importance for engineering projects associated with any subsurface infrastructure, including borehole design, hydrocarbon development, and production planning in the oil and gas industry. This chapter reviews the basic principles of petroleum geomechanics and discusses the use of mechanical earth modeling techniques to model stresses, strains, and borehole stability criteria.