The effects of mechanical stresses in the voltage hysteresis of a lithium ion battery during charge-discharge cycles is theoretically investigated. Based on the modified Butler-Volmer equation, a characteristic over-potential induced by stresses is analyzed, which shows that the compressive stress induced in an electrode surface layer would impede lithium intercalation. Therefore, a higher over-potential is needed to overcome the intercalation barrier induced by stresses. In addition, the difference between the stress induced over-potential during charging and that over discharging, i.e. hysteresis height, depends on the charge rate, the square of electrode particle radius, as well as a combined parameter that reflects the influence of material properties including elastic modulus, partial molar volume, capacity and diffusivity. The present calculations show that the induced stresses are four orders of magnitude higher in silicon electrodes compared with those in graphite and LiMn2O4 electrodes. Finally, a relaxation simulation shows that the stress variation from a thermodynamically non-equilibrium state to an equilibrium state under an open-circuit operation leads to a relaxation of the electrode potential. This serves as a proof that battery performance is affected by the induced stresses.