The sorption and diffusion of low molecular weight penetrants proceeds almost exclusively through the amorphous component of the semicrystalline polymer solid. The diffusive transport properties and geometrical distribution of the amorphous component are substantially modified by mechanical and thermal treatment. Deformation of spherulitic material first loosens the structure and then transforms it into a densely packed fibrous structure with a great many taut tie molecules in the amorphous component. Annealing lets the crystals grow in thickness, removes crystal defects, sharpens the boundaries between crystalline and amorphous component, and relaxes the taut tie molecules. The resulting changes of transport properties cannot be described in a satisfactory manner by crystallinity and orientation but requite a detailed consideration of morphology. The elastic tensile deformation enhances sorption and diffusion by reducing the density of amorphous component. The high anisotropy of diffusion and the drastic reduction of sorption and diffusion of fibrous material are the consequence of the microfibrillar morphology with the large fraction of highly aligned and closely packed taut tie molecules which eliminate many sorption sites, enormously reduce the diffusivity, and increase its concentration dependence. The anisotropy may be reduced during plastic deformation of the fibrous material by the increased number of interfibrillar tie molecules.