Molecular transport of organic liquids into Viton fluoropolymers has been investigated by a sorption-desorption gravimetric method. Diffusion coefficients have been calculated from Fick’s equation. The sorption-desorption results have been used to calculate the concentration profiles by solving Fick’s diffusion equation under suitable boundary conditions. A numerical method based on the finite difference technique was also used to calculate the concentration profiles of liquids as a function of sorption time and thickness of the Viton fluoropolymers. The dependence of sorption, desorption, diffusion, and permeation properties of the liquids on temperature showed a significant effect. The Arrhenius activation parameters have been estimated for diffusion, permeation, and sorption processes. The experimental and calculated results are discussed to study the type and nature of interactions between Viton fluoropolymers and the solvent molecules.