AbstractAmorphous polymers are assumed to possess a quasicrystalline structure with chain bundles that are locally parallel over distances ∼1 nm. Two possible types of random motion for a spherical penetrant in such a substrate are described, one type determining the jump frequency and activation energy of diffusion, the other type determining the jump length. The former quantities may be calculated from the model, but not the latter. Sorption of simple gases at low penetrant pressures is assumed to occur mostly in pre‐existing holes, both above and belowTg, and the same penetrant diffusion mechanism is assumed to hold in the two regions. The changes in apparent heat of solution and activation energy of diffusion observed atTgare explained in terms of additional hole formation with increase in temperature aboveTg. The theory is shown to be consistent with experimental diffusion data for several glassy and rubbery systems. Evidence is given that hole formation in simple polymers such as polyethylene may occur by chain “kinking”. For polymers possessing articulated side groups, however, it appears that hole formation arises principally from motions within these