We present a new mechanistic model for the self-similar propagation of case II sorption fronts of diluents into glassy polymers, The model not only presents a clear differentiation between the chemical-potential-induced driving forces and the material misfit-induced pressures that develop in the Fickian precursor field that counteract the driving forces but also set up conditions for visco-plastic extrusion of the diluent-enriched polymer out of the surface or into a zone of rubbery gel behind the case-II process front. The quantitative predictions of the model are capable of giving accurate comparisons with experimental measurements, particularly with those of Kramer and co-workers on the penetration of iodoalkanes into polystyrene.