The knowledge of mechanical properties of swelling clays on the scale of the clay layer is of crucial importance to build predictive hydromechanical macroscopic constitutive laws in a bottom-up approach. In this work, we computed the elastic properties of particles of a swelling clay (i.e., montmorillonite) by molecular dynamics simulations. Because of the softness of the material in the direction orthogonal to the clay layer with increasing water content, the computation of the whole stiffness tensor was not trivial: we needed to implement the elastic bath method,1 which allows us to attenuate thermal strains and compute the stiffness via strain fluctuations in isothermal–isobaric simulations. We investigated the effect of water content, temperature, and the interlayer cation on the elastic properties of swelling clays. In particular, we showed that the out-of-plane stiffness coefficients computed at 300 K differed significantly from the same coefficients computed at 0 K. The out-of-plane coefficients were very sensitive to both temperature and water content. In contrast, the dependence of the in-plane coefficients to temperature was slight. Moreover, the decrease of the in-plane coefficients with water content could be entirely explained by the change of geometry of the system due to the swelling of the interlayer space. The interlayer cation impacted the elastic properties of montmorillonite only in the driest states.