A free volume approach of the diffusion of organic molecules in polymers above their glass transition temperature (T-g) is addressed in this work. The idea that molecular transport is regulated by free volume was first introduced by Cohen and Turnbull [M. H. Cohen and D. Turnbull, J. Chem. Phys. 31, 1164 (1959)]. Our hypothesis is that the diffusion of small molecules, like plasticizers, in a polymer, here the copolymer of ethylene and vinyl acetate (EVA) above T-g, can be described by Fick's classical law. The experiments were carried out on a parallel plate geometry rheometer, We studied the diffusion of the diethyl 2-hexyl phtalate (DOP) into the melted EVA at four different temperatures. Using Fick's law, the concentration of the plasticizer was established for any given point of the thickness of the swelling elastomer at any time. Using a one-dimensional grid to solve continuous equations that describe the different theological contributions of each abscissa, we determined the linear viscoelastic response of the whole sample. By comparing the experimental loss modulus to the values calculated from the theological model, we found the values of the three parameters of the free volume expression of the diffusion coefficient. A simple relation which describes the mutual diffusion coefficient of DOP into melt EVA and depends exponentially on 1/T and on the weight fraction of solvent (omega(1)) was established to be D-1 = 0.157 exp(-90.3 X 10(3)/RT)exp(15.8omega(1)).