Molecular dynamics simulations are used to study the stability of structure H (sH) clathrate hydrates with the rare gases Ne, Ar, Kr, and Xe. Simulations on a 3×3×3sH unit cell replica are performed at ambient pressure at 40 and 100K temperatures. The small and medium (s+m) cages of the sH unit cell are assigned rare gas guest occupancies of 1 and for large (l) cages guest occupancies of 1-6 are considered. Radial distribution functions for guest pairs with occupancies in the l-l, l-(s +m), and (s+m)-(s+m) cages are presented. The unit cell volumes and configurational energies are studied as a function of large cage occupancy for the rare gases. Free energy calculations are carried out to determine the stability of clathrates for large cage occupancies at 100K and 1bar and 20kbar pressures. These studies show that the most stable argon clathrate has five guests in the large cages. For krypton and xenon the most stable configurations have three and two guests in the large cages, respectively.