A generalized model for permeation of multicomponent gas mixtures through polymeric membranes has been presented here. The governing transport equations are discussed for a multicomponent mixtures which can be applied in a number of situations; for example, feed flowing outside or inside of fibres; feed and permeate flowing in cocurrent or countercurrent mode. To solve the governing coupled and nonlinear differential equations the driving force approximation (DFM) method developed earlier is extended and analytical expressions are presented assuming a quadratic variation in the driving force with membrane area for all components in the mixture. This results in much simpler and faster computations. The effectiveness of the method for different conditions is discussed.