The crucial role of mechanical stress in voltage hysteresis of lithium ion batteries in charge-discharge cycles is investigated theoretically and experimentally. A modified Butler-Volmer equation of electrochemical kinetics is proposed to account for the influence of mechanical stresses on electrochemical reactions in lithium ion battery electrodes. It is found that the compressive stress in the surface layer of active materials impedes lithium intercalation, and therefore, an extra electrical overpotential is needed to overcome the reaction barrier induced by the stress. The theoretical formulation has produced a linear dependence of the height of voltage hysteresis on the hydrostatic stress difference between lithiation and delithiation, under both open-circuit conditions and galvanostatic operation. Predictions of the electrical overpotential from theoretical equations agree well with the experimental data for thin film silicon electrodes.