Performance and reliability of energy harvesting, storage and conversion devices are closely connected to mechanics as large stress gradients are usually intrinsic. In addition to causing mechanical failure, large stress is suspected to lead to anomalous experimental observations in a wide range of electrochemical cells. However, the standard framework for mixed ion-electron conductors does not capture this electro-chemo-mechanical coupling in stressed solids; it remains a challenge to theoretically predict how external stress would influence the reaction kinetics or electrical transport of solids.In this contribution, we will present a generalized thermodynamic theory to explain how and mechanics are coupled to ionic and electronic carriers in the presence of stress field. We categorize the carriers into physically-meaningful four types, based on the signs of the charge number (i.e., polarity) and the partial molar volume (i.e., expansion coefficient). Beyond the electrostatic effects discussed in the literature, our work reveals the importance of elastic effects, as demonstrated by simulations of a composite beam bending experiment. The proposed framework not only provides a deeper understanding of stress-driven phenomena in electrochemical materials, but also suggests an unconventional approach to mechanically tune the interfacial electrical properties of mixed-conducting solids.