In many polymeric controlled release systems (CRSs) the drug release kinetics is mainly ruled by the penetrant absorption characteristics which, in turn, depend on the viscoelastic properties of the polymer/penetrant system. The kinetics of the drug release process can follow either a typical Fickian behavior or a non-Fickian one (anomalous release), depending on the polymer/penetrant viscoelastic properties. The aim of this work is to model such physical evidences by means of the appropriate flux equations describing the penetrant uptake and the corresponding drug release. As a main result of our work we prove that, by resorting to the Sarti and Camera-Roda flux equation for the penetrant, and to the Fick flux equation fur the drug, it is possible to simulate both Fickian and non-Fickian drug release from swelling CRSs characterized by different viscoelastic properties of the polymer:penetrant system. Furthermore, we demonstrate that the effect of the density gradient developing inside the matrix during the drug release does not sensibly affect the drug release kinetics.