The H2S stability of a range of MOFs was systematically assessed by first-principle calculations. The most likely degradation mechanism was first determined and we identified the rate constant of the degradation reaction as a reliable descriptor for characterizing the H2S stability of MOFs. A qualitative H2S stability ranking was thus established for the list of investigated materials. Elemental structure-stability relationships were further envisaged considering several variables including the nature of the linkers and their grafted functional groups, the pore size, the nature of metal sites and the presence/nature of coordinatively unsaturated sites. This knowledge enabled the anticipation of the H2S stability of one prototypical MOF, e.g. MIL-91(Ti), which has been previously proposed as a good candidate for CO2 capture. This computational strategy enables an accurate and easy handling assessment of the H2S stability of MOFs and offers a solid alternative to experimental characterizations that require the manipulation of a highly toxic and corrosive molecule.