Monte Carlo molecular modeling simulations have been performed to investigate some of the microscopic mechanisms underlying smectite clay swelling. The systems we have studied represent hydrated Wyoming montmorillonites in which the counterions are Li+, Na+, or K+. For each of these three counterions we have conducted a series of 15 simulations in which the water content is increased systematically from 0 to 300 mg/g of clay. In this paper we introduce a new set of interaction potentials that can be used to study clay-water-cation systems and which lend themselves to future studies of intercalated organic molecules. We compare simulation data for the clay layer spacing with experimental swelling curves and find that the level of agreement is striking. Interestingly, in regions where the experimental curves exhibit hysteresis for adsorption/desorption, these loops enclose our calculated data. This indicates that our simulations indeed represent states of thermodynamic equilibrium, conditions which are harder to achieve experimentally. We are therefore content with our choice of atomistic interaction potentials for the current work. Analysis of the microscopic interlayer structure reveals a qualitative difference between Li+ and Na+ on the one hand and K+ on the other. We find that as the water content is increased, both Li+ and Na+ are able to hydrate, thereby becoming detached from the clay surface. In contrast, we find that K+ ions migrate to and bind to the clay surface during our simulations. Therefore ECC ions screen the negatively charged, mutually repelling clay surfaces more effectively than Naf and Lif ions do. The reluctance of K+ ions to fully hydrate will reduce the tendency of K+-saturated clays to expand. Our simulations therefore provide a qualitatively satisfying insight into the role of K+ ions as a clay swelling inhibitor. Indeed, the differences between Na+ and K+ ions displayed in these simulations may also be of more general relevance to colloid chemistry and physiology.