Several surface terminations for RuS2(111) have been compared on the basis of theoretical calculations. Hartree-Fock Periodic calculations with a posteriori evaluation of the correlation energy with a density functional approach have been used. The surfaces with an excess of S atoms compared to the RuS2 stoichiometry are found to be more stable, the most stable one having seven S atoms at the surface for the unit cell, Depending on the amount of surface S, the S binding energy varies in a large interval and is smaller for atoms in a S-2 pair than for isolated S atoms. Dissociation of H-2 is strongly exothermic on these surfaces, giving generally SH groups but also Ru-H bonds for highly reduced surfaces. These calculations enable the building of a model and an energy profile for the reduction process of the RuS2 surface.