Corrosion (or oxidation) of metals in ambient air produces metal oxide that is undesirable in most cases. In the case of uranium, a solid corrosion product consisting of uranium dioxide and uranium hydride is produced. Uranium hydride is pyrophoric in air and can therefore self-ignite leading to operational safety issues in nuclear waste storage facilities. In addition, hydrogen gas that is produced when uranium reacts with water vapour is potentially hazardous when it accumulates and leads to deterioration of the material. In this study, we investigate the oxidation kinetics of uranium in environments that contain oxygen or water vapour. Uranium dioxide is produced as the main corrosion product in such environments, with uranium hydride formed as a reaction intermediate in the presence of water vapour. The corrosion product is less dense than the parent metal (uranium), resulting in expansion of the material when the metal is converted to oxide or hydride. Experimental evidence indicates that the oxidation rate in water vapour is at least 5000 times larger than the rate in dry air or oxygen, suggesting different mechanisms or diffusing species. Uranium oxidation is thus a complex process involving several physicochemical processes (including advection, adsorption, diffusion, reaction and desorption), where diffusion of the oxidising species through the oxide layer adhering to the metal or hydride largely determines the overall oxidation rate. Here oxygen ions in dry air and hydroxide ions in water vapour constitute the oxidising species. In the oxidation of uranium by dry air, a self-induced electric field contributes to the diffusing flux of oxygen ions, in addition to a concentration gradient. The dry-air oxidation is modelled as a Stefan (discrete-layer) problem, where a Stefan condition provides the velocity of the moving interface (or phase boundary) that separates different homogeneous phases. The Stefan model allows for unsteady development of the concentration profile of the diffusing species in the oxide layer, which forms the novel aspect of this problem. As the underpinning chemistry becomes substantially more complex in a water-vapour environment, it is unclear how to construct an analogous Stefan problem (or even if one exists). For the water-vapour corrosion of uranium, a one-dimensional reaction-advection-diffusion (RAD) problem is formulated as a new model based on a proposed reaction scheme involving at least two diffusing and three static components. A distinguishing feature in the RAD model compared to the Stefan model is the presence of reaction fronts which are transition (or mixed-phase) regions. The RAD model is tackled using both numerical and asymptotic approaches, wherein two diffusion layers and two reaction fronts are found in the large-time asymptotic solution. Asymptotic matching across the different regions (or layers) provides analytical predictions for the thickness of the diffusion layers, locations of the propagating reaction fronts and concentration profiles in the diffusion layers. The numerical solution strategy utilises a Howarth-Dorodnitsyn transformation to allow for volumetric expansion during corrosion. The full numerical solution is found to be consistent with the asymptotic predictions, showing that a few-nanometres-thick propagating hydride layer that is bounded by a pair of coupled reaction fronts is possible in the RAD model. A parabolic (square-root time dependence) oxidation regime is found at the early stages of oxidation, whereas the late stages (i.e. after cracking or spalling of the surface oxide) follow linear kinetics in both dry air and water vapour environments. The influence of parameters associated with the diffusion coefficients, material properties and the external gas state on the oxidation kinetics is investigated. For the water-vapour oxidation of uranium, even though the oxide formation relies on the presence of an intermediate hydride phase, its thickness is found to be dependent only on the material properties and the external water vapour state. The RAD model is a first mechanistic model of uranium oxidation in water vapour and gives qualitative predictions that are consistent with the recent experimental observations using atom-probe tomography.