In this paper we present a coupled thermodynamic formulation to predict stresses, in an ionic solid due to diffusion of charged defects in an electrochemical potential gradient. Chemical expansion is considered primarily by treating compositional strains as eigen strains. Two material properties are introduced a) A second order tensor that represents the eigen strains in the solid due to non-stoichiometry and b) A fourth order tensor that represents the variations in elastic properties due to non-stoichiometry. A general theory is first developed for a steady state, isothermal condition, while considering typical electrochemical reactions at the interface and the bulk of a typical oxide ion conductor by considering all the major defects that are known to operate. Two geometries typical of solid electrolytes (planar and tubular) are considered, involving diffusion of vacancies and electrons. The governing equations are solved for the resulting stresses due to chemically induced strains resulting from a deviation in the stoichiometric composition of the solid. The results show the influence of considering the coupled problem on the distribution of defects, electrostatic potential, and the current voltage characteristics.