In this paper, we present quantum mechanical (QM) calculations, at a periodic Hartee-Fock (HF) level, on the bulk and surface properties of cubic CeO2 and ZrO2. We have investigated the M-O bending features, and established the high degree of ionicity of both materials, which is greater for CeO2 than ZrO2. The calculated values for the C-11, C-12, and C-44 elastic constants, are in close agreement with experiment; an extended oxygen basis set, containing d-orbital polarization functions, is essential to model accurately the symmetry lowering during the C-44 distortion. In the surface studies, we have calculated the surface energies of the {011} and {111} faces of both ceria and zirconia. QM results are compared with interatomic potential-based (IP) methods to assess the accuracy of the latter. We found that IP methods provide a correct estimate of the surface relaxations and the correct order of stability of the two faces examined, with the energy difference between the {011} and the {111} surfaces being approximately 1 J/m(2), as in the QM study, However, IP methods do not always discriminate adequately between the properties of the two materials. Finally, we found that geometric and electronic relaxations in the {111} surface are confined to the outermost oxygen ions, while in the {011} slabs they are more important and extend to the subsurface layers in a columnar way, The unsaturation of the surface ions in the {011} face may have important implications for the catalytic activity of the materials.