A new mass transfer model for layered structures, based on an implicit multistep integration algorithm including concentration-dependent diffusivities, has been developed and applied to systems of water diffusing in electron beam pre-irradiated, acrylamide-grafted aliphatic polyesters (poly(epsilon-caprolactone) and poly(1,5-dioxepan-2-one)). The much higher water solubility and water diffusivity in the amorphous crosslinked poly(1, 5-dioxepan-2-one) than in the semicrystalline poly(epsilon-caprolactone) is explained as being due to the fact that crystals are more effective crosslinks than the chemical crosslinks. Water solubility in the grafted layer is a function of the concentration of polyacrylamide, but it is believed to be limited by compressive swelling-induced stresses. The zero concentration water diffusivity in the graft layer passes through a maximum, whereas the graft-layer density passes through a minimum with increasing acrylamide concentration. It is suggested that this is because the accessible free volume for the penetrating water molecule is increased in the initial stages of grafting because the matrix polymer chains are separated by growing acrylamide graft chains. At later stages, the accessible free volume decreases because additional polyacrylamide chains are growing adjacent to the already existing ones and thus fill up empty spaces.