The energy of formation and the Lewis acid strength of sulfur vacancies or coordinative unsaturated sites on the MoS2 edges were studied using density functional theory for periodic systems and an electrostatic potential-based methodology. The results suggest that the more energetically favorable sites are located on the sulfur edges; however, their Lewis acid strength is considerably smaller than the site acidity at the molybdenum edges. The acid strength for the reported most hydrodesulfurization active site of RuS2 was also determined. In general, the Lewis acid for the site on RuS2 is 100% smaller than the sites on the Mo edges and around 20% larger than the most favorable site on the S edges of MoS2. Binding of the pyridine molecule in the 77, adsorption configuration on the considered sites has corroborated the trend of Lewis acidity suggested by the electrostatic potential methodology.