This paper describes the oxidation of iron-rich uranium-bearing rocks by infiltration of ground-water. A reaction-diffusion model is set up to describe the sequence of reactions involving iron oxidation, uranium oxidation and reduction, sulphuric acid production, and dissolution of the host rock that occur. On a geological timescale of millions of years, the reactions occur very fast in very thin reaction fronts. It is shown that the redox front that separates oxidized (orange) rock from reduced (black) rock must actually consist of two separate fronts that move together, at which the two separate processes of uranium oxidation and iron reduction occur, respectively. Between these fronts, a high concentration of uranium is predicted. The mechanics of this process are not specific to uranium-mediated redox reactions, but apply generally and may be used to explain the formation of concentrated ore deposits in extended veins. On the long timescales of relevance, a quasi-static response results, and the problem can be solved explicitly in one dimension. This provides a framework for studying more realistic two-dimensional problems in fissured rocks and also for the future study of uraninite nodule formation.