Predicting the absorption of gases and liquids in semicrystalline polymers is of critical importance for numerous applications; the mechanical and transport properties of these materials are highly dependent on the amount of solutes dissolved in their bulk. For most semicrystalline polymers which are in contact with an external fluid, the observed uptake of the solute is found to be lower than that predicted by treating the amorphous domains of the polymer as subcooled polymer melts at the same thermodynamic state. This observation has recently led to the hypothesis that the amorphous domains effectively behave as polymer liquids subject to an additional “constraint pressure” which reduces the equilibrium solubility in the domains. We present a new statistical mechanical model of semicrystalline polymers. The constraint pressure emerges naturally from our treatment, as a property of the interlamellar amorphous domains caused by the stretching and localization in space of the tie-molecules (polymer chains linking different lamellae). By assuming that the interlamellar domains exchange monomers reversibly with the lamellae, the model allows one to simultaneously predict the increase of constraint pressure at low temperatures and the variation of the lamellar thickness as a function of temperaturea phenomenon known as premelting. The sorption isotherms of a range of fluids in different polyethylene and polypropylene samples are determined experimentally and the data is compared with calculations of the new model using the SAFT-VR Mie EoS. In order to accurately predict the absorption close to the vapor pressure of the penetrant, we find that it is essential to include the “free”, unconstrained amorphous domains in the description, resulting in a multiscale model with two adjustable parameters (the fractions of tie-molecules and free amorphous domains) that characterize the morphology of a given semicrystalline polymer sample. The trends observed for the adjusted parameters qualitatively match other estimates reported in the literature.