We analyze the effects of mechanical stresses arising in a solid polymer electrolyte (SPE) on the electrochemical performance of the electrolyte component of a lithium ion battery. The SPE is modeled with a coupled ionic conduction-deformation model that allows to investigate the effect of mechanical stresses induced by the redistribution of ions. The analytical solution is determined for a uniform planar cell operating under galvanostatic conditions with and without externally induced deformations. The roles of the polymer stiffness, internally-induced stresses, and thickness of the SPE layer are investigated. The results show that the predictions of the coupled model can strongly deviate from those obtained with an electrochemical model—up to +38% in terms of electrostatic potential difference across the electrolyte layer—depending on the combination of material properties and geometrical features. The predicted stress level in the SPE is considerable as it exceeds the threshold experimentally detected for irreversible deformation or fracture to occur in cells not subjected to external loading. We show that stresses induced by external solicitations can reduce the concentration gradient of ions across the electrolyte thickness and prevent salt depletion at the electrode-electrolyte interface.