This work focusses on the study of the diffusion of vegetable oils and their derivatives in thermoplastic polymers. For this purpose, it was designed by chemical modification of soybean and rapeseed oils new vegetable oils able to mimic fossil substrates such as mineral oil (Torilis (R)) and diisononylphthalate (DINP) used in EPDM and PVC plastisols respectively. The first aim of this paper is to examine the Hansen solubility parameters in diffusion experiments in order to identify the strengths and weaknesses of this method. Furthermore, the diffusion ability of these vegetable molecules was studied experimentally using rheological methods. Actually, such rheological methods proved necessary to definitively select the most suitable molecules in terms of their viscosity as the diffusion process is mainly viscosity dependent. To conclude, the studied methods, solubility parameters determination and rheological experiments, are complementary to select suitable modified vegetable oils in terms of their diffusion in thermoplastic polymers. (C) 2017 Elsevier B.V. All rights reserved.