We study the effect of mechanical stresses arising in solid polymer electrolytes (SPEs) on the electrochemical performance of lithium-ion (Li-ion) solid-state batteries. Time-dependent finite element analyses of interdigitated plate cells during a discharge process are performed with a constitutive model that couples ionic conduction within the SPE with its deformation field. Due to the coupled nature of the processes taking place in the SPE, the non-uniform ionic concentration profiles that develop during the discharge process induce stresses and deformations within the SPE; at the same time the mechanical loads applied to the cell affect the charge conduction path. Results of a parametric study show that stresses induced by ionic redistribution favor ionic transport and enhance cell conductivity—up to a 15% increase compared to the solution obtained with a purely electrochemical model. We observe that, when the contribution of the mechanical stresses is included in the simulations, the localization of the electric current density at the top of the electrode plates is more pronounced compared to the purely electrochemical model. This suggests that electrode utilization, a limiting factor for the design of three-dimensional battery architectures, depends on the stress field that develops in the SPE. The stress level is indeed significant, and mechanical failure of the polymer might occur during service.