A mathematical model describing the extraction of uranium(VI) from sulfuric acid solutions into polymer inclusion membranes composed of di(2-ethylhexyl) phosphoric acid (D2EHPA) and poly(vinyl chloride) (PVC) has been developed and numerically solved. It assumes ideal mixing in the solution and Fickian diffusion of the uranium(VI)-D2EHPA complex within the membrane. The model has been fitted to transient extraction data obtained for different membrane compositions and thicknesses and different initial solution concentrations of uranium(VI) and sulfuric acid. This has allowed a reliable determination of the membrane extraction constant (K-ex = 4.72 x 10(3)) and diffusion coefficient (D-m = 4.13 x 10(-14), 6.46 x 10(-14) and 7.39 x 10(-14) m(2) s(-1) for membranes containing 35%, 40% and 45% (mm) D2EHPA, respectively). The very good agreement between the model and the experimental extraction data confirms the model's validity. This model provides an in-depth understanding of the physicochemical processes involved in the extraction of uranium(VI) into D2EHPA/PVC PIMs and can be used for the optimization of this process using numerical simulation. (c) 2012 Elsevier B.V. All rights reserved.