Density functional theory (DFT) is used to investigate the reaction pathways for H2S adsorption on Au(111) and Cu(111) at low coverage as well as the full decomposition of H2S on Cu(111). On both surfaces, a weakly bonded molecular state is found with the S atom bond on top sites being molecular adsorption, a nonactivated process. The H-SH dissociation process is endothermic on Au(111), and all reaction pathways present high activation energy barriers which explains the extremely low dissociation probability of H2S on defect-free Au(111) estimated from experiments. This scenario slightly changes for H2S/Cu(111): (i) dissociated configurations are energetically more favorable than the molecular state and (ii) the H-SH bond cleavage process presents a relatively small activation energy barrier. This is not inconsistent with low but nonzero reactive sticking probability of thermal H2S molecules reported in experiments. The complete energy profile for the H2S adsorption and full decomposition is compatible with the accumulation of S-adatoms observed experimentally.