In this Communication, we use density functional theory (DFT) to examine the fracture properties of ceria (CeO2), which is a promising electrolyte material for lowering the working temperature of solid oxide fuel cells. We estimate the stress-strain curve by fitting the energy density calculated by DFT. The calculated Young's modulus of 221.8 GPa is of the same order as the experimental value, whereas the fracture strength of 22.7 GPa is two orders of magnitude larger than the experimental value. Next, we combine DFT and Griffith theory to estimate the fracture strength as a function of a crack length. This method produces an estimated fracture strength of 0.467 GPa, which is of the same order as the experimental value. Therefore, the fracture strength is very sensitive to the crack length, whereas the Young's modulus is not.