Mixed ionic electronic conductors (MIEC) have gained importance recently due to their roles in energy conversion devices such as solid oxide fuel cells (SOFC). Recent experimental data have shown that an increased vacancy concentration in a MIEC changes its elastic modulus and causes volumetric expansion. Since the MIEC in a device is constrained mechanically, the volumetric changes can induce substantial mechanical stresses. Such stresses not only lead to premature failure but can also alter the electrochemical performance of the device. In order to fully understand the interactions between stresses and defect transport a coupled theory is needed. This thesis develops a framework to study stress-defect transport interactions. The framework is based on a proper construction of the stress dependent electrochemical potential by introducing two material properties, namely the coefficient of chemical expansion (CCE) and the open system elastic constants (OSEC). The CCE characterizes the strains due to non-stoichiometry while the OSEC represents the stoichiometry dependent elastic stiffness. In this work these parameters are determined using atomistic simulations. The system of equations that govern the coupled electrochemical and mechanical fields is solved using a combination of numerical and analytical techniques. The developed solutions are analyzed to provide insights into the nature and the extent of the interactions. It is found that the non-stoichiometry-induced stress is in the same order of magnitude or even higher than that induced by thermal mismatch in a typical SOFC. In the vicinity of material flaws (cracks, voids, etc.), such stresses are further intensified which may cause fracture of the MIEC. In addition, non-stoichiometry-induced stresses can significantly alter the distribution of point defects, thus affecting the electrochemical performance of the ionic device. Furthermore, the non-stoichiometry induced stresses increases the thickness of the surface charge layer. The thermodynamic framework and the computational algorithms developed in this work provides effective methodologies and tools to analyze stress-defect transport interactions in ionic solids for designing and reliability analysis of ionic devices such as fuel cells, oxygen pumps, chemical sensors, etc.