Pressurised and boiling water reactors contain zirconium alloys, which are used as nuclear fuel cladding. Oxidation of these alloys, and the associated hydrogen pick-up, is a limiting factor in the lifetime of the fuel. To extend the burn-up of nuclear fuel requires control of the oxidation, and therefore development of a mechanistic understanding of the cladding corrosion process. Synchrotron X-ray diffraction (S-XRD) has been used to analyse oxide layers formed during in-situ air oxidation of Zircaloy-4 and ZIRLO™. Analysis shows that as the oxide thickness increases over time there is a relaxation of the stresses present in both the monoclinic and meta-stable tetragonal phases, and a reduction in the tetragonal phase fraction. To better understand the mechanisms behind stress relaxation in the oxide layer, finite element analysis has been used to simulate mechanical aspects of the oxidation process. This simulation was first developed based on stress relaxation in oxides formed in autoclave, and analysed ex-situ using S-XRD. Relaxation mechanisms include creep and hydrogen-induced lattice strain in the metal substrate and creep in the oxide layer. Subsequently the finite element analysis has been extended to stress relaxation observed by in-situ S-XRD oxidation experiments. Finite element analysis indicates that the impact of creep in the oxide is negligible, and the impact of both creep and hydrogen-induced lattice strain in the metal substrate metal is small. The implication is that stress relaxation must result from another source such as the development of roughness at the metal-oxide interface, or fracture in the oxide layer.