A model for the permeability of gases through block copolymer membranes with lamellar microstructure is developed. The model is presented in a generalized form which can also be applied to partially oriented systems with the use of an appropriate probability function for the frequency of occurrence of a particular orientation of the lamella which may be obtainable from independent experiments. The equations for the permeability of systems with perfect orientation (parallel and series) and random orientation are special cases of this model.