The presence of a limited amount of H2S in H-2-rich feed adversely affects the Pd-Cu membrane permeation performance due to the sulphidization of the membrane surface. A theoretical model was proposed to predict the S-tolerant performance of the Pd-Cu membranes in presence of H2S under the industrial water-gas-shift (WGS) reaction conditions. The ideas of surface coverage and competitive adsorption thermodynamics of H2S and H-2 on Pd-Cu surface were introduced in the model. The surface sulphidization of the Pd-Cu membranes mainly depended on the pressure ratio of H2S to H-2, temperature and S-adsorbed surface coverage, i.e., the occurrence of sulphidization on the surface was not directly related with the bulk compositions and structures [body centered cubic and face centered cubic (bcc or fcc)] of Pd-Cu alloy membranes because of the surface segregation phenomena. The resulting equilibrium equations for the H2S adsorption/sulphidization reactions were solved to calculate the pressure ratio of H2S to H-2 over a wide range of temperatures. A validation of the model was performed through a comparison between lots of literature data and the model calculations over a rather broad range of operating conditions. An extremely good agreement was obtained in the different cases, and thus, the model can serve to guide the development of S-resistant Pd alloy membrane materials for hydrogen separation.