A new pressure drop equation has been developed from the continuity equation and the momentum balance equations with the consideration of gas compressibility and fibre permeability. For the case of negligible permeation flux, the pressure equation reduces to the Hagen-Poiseuille equation. The effects of design variables such as membrane permeability and fibre radius on the pressure profiles and stage cut obtained from the two pressure models have been discussed. In addition, the effects of using the two pressure models, feed mode and membrane selectivity on operating variables such as the pressure ratio across the membrane and stage cut have also been studied. Numerical solutions of the two pressure models have been obtained for the separation of a volatile organic vapour from N-2 stream for the countercurrent flow pattern. The use of the Hagen-Poiseuille equation will result in either an overestimation or underestimation of the membrane area required at the stipulated stage cut depending on the feed mode operation.