Data obtained by sorption and permeation measurements of liquid propane in medium-density polyethylene were analyzed with an analytical diffusion model, assuming a constant diffusion coefficient, and a numerical model, based on the free volume theory of Fujita. The stress-strain properties of propane-swollen medium-density polyethylene were recorded in an Instron tensile tester. The sigmoid sorption curves (modeled here for the first time) were adequately described using nonstationary boundary conditions. The numerical model was capable of representing sorption, desorption, and permeation data, whereas the analytical technique gave satisfactory results only for sorption/desorption data in the initial, transient stage. The difference between diffusion coefficients determined from sorption and desorption measurements and the time dependence of the modulus-solute concentration relationship can be explained by assuming a relaxation of constrained amorphous chain segments. The penetrant-induced structure rearrangement is, according to differential scanning calorimetry measurements, confined to the amorphous phase.