During my PhD, I worked on diffusion-driven oxidation in metals, particularly uranium. The oxidation (or corrosion) kinetics of uranium under different environments such as oxygen and water vapour was investigated. The corrosion product is less dense than the parent metal which results in an expansion of the material when the metal is converted to oxide or hydride. Uranium oxidation is hence a complex process involving several physicochemical processes (including advection, adsorption, diffusion, reaction and desorption), wherein diffusion of the oxidising species through the oxide layer adhering to the metal or hydride was found to largely determine the overall oxidation rate. Different approaches were used to model uranium corrosion in the aforementioned environments. 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 non-diffusing components. Both numerical and asymptotic approaches were used.