The effects of mechanical stresses on the voltage hysteresis of a lithium ion battery during charge-discharge cycles are theoretically investigated. A diffusion-reaction-stress coupling model has been established. It is found that a compressive stress in the electrode surface layer would impede lithium intercalation. Therefore, a higher overpotential is needed to overcome the intercalation barrier induced by stresses. The stress difference between charge and discharge made contribution to the voltage hysteresis which depends on charge rate, 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. Calculations show that the stress-induced overpotentials are several orders of magnitude higher in silicon electrodes compared to 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 leads to the relaxation of the electrode potential under an open-circuit operation. This serves as a proof that battery performance is affected by stresses.