Barrier properties of polymer films can be improved in various ways, such as formation of multilayer structures by coextrusion, surface treatment, and coatings. This work explores the use of thousands of alternating layers of polymer (xyxy...) to modify the resistance to permeation. A model is presented to predict the number of layers needed in a laminate to change the flux of a permeant by a given amount. An important feature of the model is the species transport across the interdiffusion regions at the polymer-polymer interfaces where diffusivity of the penetrant, D-i, is assumed to be a constant or a function of the volume fractions (phi) of the interdiffusing polymers. For constant D-i, the modeling results show that increasing the number of interfacial regions decreases the flux for a given condition, and a large number of layers are required to achieve appreciable flux reduction. For phi-dependent D-i, a balanced interdiffusion region was modeled in which the interdiffusing polymers were assumed to interpenetrate one another equally. In this particular case, the flux was predicted to always increase with the number of layers.