Most tests of the dissolution behavior of glasses quote the leach rate, often measured in flowing solutions. In the past, it has been pointed out that this may not be the rate-determining factor for the dissolution of glass in a radioactive waste repository because of the very small flow rate of water past the glass surface. Under these conditions, the rate of removal of elements from the glass would be controlled by the flow rate and the effective saturation solubility of the glass in the water, or, in stagnant conditions, by the rate of diffusion of species dissolved in the water away from the glass surface. Simple quantitative models are developed to provide a framework for the discussion of these effects, and they indicate that in cases of practical importance it is indeed solubility and either water access or diffusion that together limit the rate of dissolution of the glass. It can be concluded that effective leach rates in a repository will be below 10−7g.cm−2. day −1, a figure that in other studies has given a clear margin of long-term safety for radiological purposes.