Analytical expressions are presented for calculating the extent of separation of binary gas mixtures achievable in a permeation stage, as well as the required membrane area, when the high- and low-pressure streams in the stage flow either countercurrently or cocurrently to each other. The derivations are similar to those of Oishi et al., but are cast in a form suitable for computer calculations. The results of a parametric study on the separation of oxygen from air are presented for four different flow patterns inside the stage: (a) countercurrent flow, (b) cocurrent flow, (c) cross-flow, and (d) perfect mixing. In the first three cases it is assumed that no mixing occurs on the two sides of the stage (or membrane). The type of flow in the permeation stage can have a significant effect on the degree of separation, but has relatively little effect on the membrane area at low separation factors. Countercurrent flow is the most efficient flow pattern, whereas perfect mixing is the least efficient one, both from the viewpoints of extent of separation and membrane area requirements.