A 2D mathematical model was developed to study liquid extraction by membrane contactors. The extraction system included a hollow-fiber membrane extractor, an aqueous solution of ethanol and acetone as the feed, and a near-critical phase of carbon dioxide as the solvent. Axial and radial diffusions of the ethanol and acetone within the tube side, through the membrane, and within the shell side of the contactor were considered in the model. The equations of the model were solved by a numerical method based on the finite element method (FEM). The predicted results of the extraction for ethanol and acetone show an average difference of 15.66% and 2.55% with the experimental data, respectively. Simulation results for extraction of acetone are more accurate than those for ethanol mostly due to a better estimation of the transport properties within the aqueous phase, which controls extraction of this solute. The developed mass transfer model is more accurate than the other few provided models in the literature and represents a general approach which can be applied for similar membrane separation systems.