Cerium oxide doped with gadolinium is an attractive electrolyte material for solid oxide fuel cells (SOFCs) operating in the temperature range 500-800 degrees C. Under the low oxygen activity conditions of the SOFC anode the ceria is partially reduced and its lattice parameter increases leading to the generation of stress in the electrolyte. These stresses have been calculated for a range of different parameters (Gd doping level, temperature, oxygen activity and cell current) and for different geometrical configurations of an initially planar electrolyte membrane (self-supported or supported on a porous substrate). The calculations show how the maximum tensile stresses are related to the non-stoichiometry of the electrolyte. The calculations also show that self supporting planar electrolytes should be allowed to relax by bending in order to minimise the risk of fracture and that supported electrolytes should be made as thin as possible. The calculations indicate that the maximum ’safe’ operating temperature for Ce0.8Gd0.2O1.9-delta at an anode oxygen activity of 10(-20) is about 750 degrees C. The limitations of assumptions made in the calculations are discussed.