The durability of concretes in radioactive waste repositories is likely to be limited by their reaction with sulphate-bearing groundwaters. In such a situation the concrete slowly degrades by sulphate penetrating into the concrete where it reacts with the cement to cause stress and eventual disruption. Experiments have been carried out to quantify these reactions and the resulting expansions. The data have been incorporated into an overall mechanistic model for sulphate degradation in which the criterion for disruption is the accumulation of a critical amount of stored elastic energy in the reaction zone. The results of this model are in good agreement with those of an earlier empirical model and enable extrapolations to be made to different concretes and groundwaters.