Terpenes such as d-limonene, alpha-pinene and p-cymene are considered green solvents that have no harmful effects on human health and the environment. These solvents represent promising alternatives for many recently classified harmful solvents such as n-hexane, the typical solvent used for the extraction of vegetable oils. Although terpenes show high solvation power for the different oil constituents, their recovery by conventional evaporation stands as a barrier for their large-scale utilisation as they have significant higher boiling points than n-hexane. In this work, the transport of terpenes through a composite polydimethylsiloxane/polyacrylonitrile (PDMS/PAN) membrane is investigated at different experimental conditions. A nonlinear increase in the solvent flux was observed with increasing transmembrane pressure which could be explained by the solution-diffusion model in a highly swollen membrane. The highest fluxes were observed with d-limonene followed by p-cymene then alpha-pinene. The sorption equilibria and diffusion coefficient of the terpenes in free-standing PDMS films were also studied and this data used to successfully model the permeation data. The performance of the PDMS/PAN membranes was stable after storage in the solvents for one year. The results obtained from this study indicate potential utilisation of solvent resistant nanofiltration for the recovery of terpenes with minimal energy consumption.