A defect model for UO$_2$ fuel containing soluble fission products was devised based on the defect structure of pure and doped uranias. Using the equilibrium between fuel solid-solution and fission-products and the material balance within the fuel, a tracing method to get the stoichiometry change of urania fuel with burnup was made. This tracing method was applied to high burnup urania fuel and DUPIC fuel. The oxygen potential of urania fuel turned out to increase slightly with burnup. The stoichiometry change was calculated to be negligible due to the buffering role f Mo. The oxygen potential of DUPIC fuel out to be sensitive to the initial chemical state of Mo in the fuel.