Molybdenum disulfide, in particular its edges, has attracted considerable attention as possible substitute for platinum catalysts in the hydrogen evolution reaction (HER). The complex nature of the reaction complicates its detailed experimental investigations, which are mostly indirect and sample dependent. Therefore, density functional theory calculations were employed to study how the properties of the MoS2 Mo-edge influence the thermodynamics of hydrogen adsorption onto the edge. The effect of the computational model (one-dimensional nanostripe), border symmetry imposed by its length, sulfur saturation of the edge, and dimensionality of the material are discussed. Hydrogen adsorption was found to depend critically on the coverage of extra sulfur at the Mo edge. The bare Mo-edge and fully sulfur-covered Mo-edge are catalytically inactive. The most favorable hydrogen binding towards HER was found for the Mo-edge covered by sulfur monomers. This edge provides hydrogen adsorption free energies positioned around -0.25eV at up to 50% hydrogen coverage, close to the experimental values of overpotential needed for the HER reaction.