It is well known that gadolinium doped ceria (GDC), when subjected to reducing conditions, undergoes significant volumetric expansion and changes its elastic stiffness. In this paper, a methodology based on a semi-analytical formulation in conjunction with molecular dynamic (MD) simulation is presented to determine the coefficient of compositional expansion (CCE) and the complete elastic stiffness tensor of two common forms of GDC at various levels of non-stoichiometry and temperatures. The CCE is determined by comparing the volumes of the MD simulation cell before and after the reduction at a given temperature. To compute the elastic constants, MD simulations are first conducted to determine the equilibrium (relaxed) positions of each atom. Then, the constants are obtained through an analytical method that uses the relaxed positions of the atoms in the simulation cell. It is found that the elastic stiffness tensor of the non-stoichiometric structures remain cubic. The elastic constant C11 decreases with increasing vacancy concentration, while the changes in C12 and C66 were found to be negligible. In addition, both the elastic constants and the CCE are found to be insensitive to temperature. © 2009 IOP Publishing Ltd.