In this work the Na-montmorillonite hydrates are studied for different burial depths by means of hybrid Monte Carlo (HMC) and molecular dynamics (MD) simulations. The HMC simulations, performed using a NPzzT ensemble, allow us to study the interlaminar space distance, structural properties, and thermodynamical properties, such as the water chemical potential. The latter quantifies the system affinity for water, and hence, it is useful for determining the most probable hydration states for a given basin condition. For increasing burial depth, we found many agreements with experimental results such as a tendency to dehydration, an increasing disorder of the interlaminar space, and a constant coordination number for the first water shell around Na+. The MD simulations, on the other hand, were performed employing a microcanonical ensemble, from which the diffusion coefficients for water and Na+ were also investigated for high-temperature and high-pressure conditions.