Ceramic oxygen-transportmembranes, such as the doped perovskite La0.6Sr0.4Co0.8Fe0.2O3-delta (LSCF6482) considered in the present paper, are effective in applications such as air separation. The present paper considers a planar configuration that is composed of a thin (order tens of microns) ion-transport membrane, a relatively thick (order millimeter) porous-ceramic support structure, and millimeter-scale oxygen-collection flow channels. The lattice-scale strain associated with charged defects (oxygen vacancies and small polarons) within ion-transport membranes causes macroscopic stress that could distort or damage the assembly. The modeling approach is based on an extended two-dimensional Nernst-Planck-Poisson (NPP) formulation that is developed and applied to evaluate the effects of chemically induced stress within a planar oxygen-separation assembly. The computational model predicts two-dimensional distributions of steady-state defect concentrations, electrostatic potentials, and stress. Parameter studies consider the effects of support-membrane dimensions, materials mechanical properties, and operating conditions. Although the stress is found to have a negligible influence on the defect transport, the defect transport is found to significantly affect the stress distributions. Such results can play important roles in the design and development of planar ion-transport membranes and their support structures. (C) 2017 The Electrochemical Society. All rights reserved.