Reaction mechanisms for the interactions between CeO2(111) and (110) surfaces are investigated using periodic density functional theory (DFT) calculations. Both standard DFT and DFT+U calculations to examine the effect of the localization of Ce 4f states on the redox chemistry of H2- CeO2 interactions are described. For mechanistic studies, molecular and dissociative local minima are initially located by placing an H2 molecule at various active sites of the CeO2 surfaces. The binding energies of physisorbed species optimized using the DFT and DFT+U methods are very weak. The dissociative adsorption reactions producing hydroxylated surfaces are all exothermic; exothermicities at the DFT level range from 4.1 kcal mol-1 for the (111) to 26.5 kcal mol-1 for the (110) surface, while those at the DFT+U level are between 65.0 kcal mol-1 for the (111) and 81.8 kcal mol-1 for the (110) surface. Predicted vibrational frequencies of adsorbed OH and H2O species on the surfaces are in line with available experimental and theoretical results. Potential energy profiles are constructed by connecting molecularly adsorbed and dissociatively adsorbed intermediates on each CeO2 surface with tight transition states using the nudged elastic band (NEB) method. It is found that the U correction method plays a significant role in energetics, especially for the intermediates of the exit channels and products that are partially reduced. The surface reduction reaction on CeO2(110) is energetically much more favorable. Accordingly, oxygen vacancies are more easily formed on the (110) surface than on the (111) surface.