In this work is reported a periodic density functional theory study of the vacancy formation mechanism on the [10-10] and the [-1010] edges Of MoS2 nanocrystallites that are the active phases in hydrodesulfurization catalysis. It has been previously shown that, from a thermodynamic point of view, there should be only very few vacancies on these edges and that their number is only slightly influenced by an increase in the hydrogen partial pressure. The kinetics of the vacancy creation is now considered through a detailed analysis of the intermediates and transition states found on the different pathways for the extraction of a surface sulfur atom by a hydrogen molecule of the gas phase. Only on one of the crystallite edges, the (10-10) (metallic edge), does the activation energy of the rate determining step of the vacancy formation remain smaller than I eV. This value allows us to consider that a dynamic equilibrium takes place on this edge. The rate-determining step is the heterolytic dissociation of the H-2 Molecule, leading to the formation of one S-H and one Mo-H group. The activation energy for the H2S departure is estimated to be 0.50 eV, in nice agreement with the value deduced from sulfur exchange experiments. The vacancy formation is possible on the [-1010] edge of the crystallite (the sulfur edge) but the rate determining step, which is the displacement of one S-H group on the surface, has an activation energy of 1.25 eV. This kind of vacancy formation on the sulfur edge does not imply the departure of one H2S molecule from the surface.