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Anhydritic claystones are among the most problematic rocks in tunnelling. Their swelling has caused serious damage and high repair costs in a number of tunnels, especially in Switzerland and southwest Germany. The swelling is usually attributed to the transformation of anhydrite into gypsum. It is a markedly time-dependent process which might take several decades to complete in nature. The present paper focusses on simultaneous anhydrite dissolution and gypsum precipitation in a closed system, i.e. disregarding the transport processes that may also be important for the evolution of the swelling process. The paper begins with a presentation of the governing equations and continues with parametric studies in order to investigate the role of the initial volumetric fractions of the constituents and the specific surface areas of the minerals involved. A simplified model for the hydration of anhydrite is also proposed, which identifies the governing process and the duration of the swelling process. Finally, parametric studies are performed in order to investigate the effect of the anhydrite surface being sealed by the formation of gypsum. The latter slows down the swelling process considerably.