In this work a counter current hollow fibre module with feed entering to shell was studied in order to separate carbon dioxide from methane. New mathematical methods for prediction of specifications of permeate and retentate streams at various conditions were developed The effects of operating and design variables on module efficiency for a mixture of CO2 and CH4 were studied It was found that sweep pressure has inverse and direct effects on the CH4 concentration in the retentate and permeates streams, respectively The opposite effect was observed for CO2.