Proton-hole mixed conductor, SrCe0.95Yb0.05O3-alpha(SCYb), has the potential to be used as a membrane for dehydrogenation reactions such as methane coupling due to its high C-2-selectivity and its simplicity for fabricating reactor systems. In addition, the mixed conducting membrane in the hollow fibre geometry is capable of providing high surface area per unit volume. In this study, mechanism of methane coupling reaction on the SCYb membrane was proposed and the kinetic parameters were obtained by regression of experimental data. A mathematical model describing the methane coupling in the SCYb hollow fibre membrane reactor was also developed. With this mathematical model, various operating conditions such as the operation mode, operation pressure and feed concentrations affecting performance of the reactor were investigated. The simulation results show that the cocurrent flow in the reactor exhibits higher conversion of methane and higher yield of ethylene compared to the countercurrent flow. In order to achieve the highest C-2 yield, especially of ethylene, pure methane should be used as feed and the operating pressure be 300 kPa. Air can be used as the source of oxygen for the reaction and its optimum feed velocity is twice of the methane feed velocity. The air pressure in the lumen side should be kept the same as or slightly lower than the pressure of shell side.