In the present study the application of a liquid membrane for selective removal of H2S from gases also containing CO2 was investigated. The liquid membrane was filled with pure methyl-di-ethanol-amine (MDEA). A theoretical model was developed to describe: (a) the chemical equilibrium between the dissolved gas and MDEA in the membrane and (b) the physical equilibrium between the solute (CO2 and H2S) in the gas and the liquid phase. Experimentally H2S and CO2 fluxes were determined in a setup consisting of two well mixed gas phase compartments separated by a flat liquid membrane. The fluxes were interpreted with the theoretical model and separately measured physical constants (solubility, diffusivity and the porosity/tortuosity factor of the membrane material). No reaction of CO2 with MDEA was observed which is attributed to the absence of water. A weak acid/base interaction of H2S and MDEA was found to increase the H2S transport through the membrane which includes higher selectivity. This effect is more pronounced at lower partial pressures of H2S.