Many oxygen-ion conducting ceramics for potential application as membranes in solid oxide fuel cells, oxygen separators and partial oxidation reactors, suffer from a chemically-induced stress when subjected to a gradient in the thermodynamic activity of oxygen. The relationships between the oxide properties, the membrane operating conditions, the membrane geometry and the resulting stresses are explored. Ceria and acceptor-doped lanthanum chromite are given as typical examples for which relevant materials data have been published. Analysis of the experimental data shows that although the lattice expansion on reduction, that gives rise to the stress, depends mainly on the deviation from stoichiometry in their oxide, the crystal structure and the dopant also have a significant influence. The induced stresses are predicted to be lowest for planar membranes that are free to bend in order to relax the stresses. However, the stresses in a planar membrane that is constrained not to bend are predicted to be similar to those induced in a tubular membrane.