The primary objective of this article is to develop an analytic procedure for calculating the permeation fluxes of mixtures of penetrant molecules across polymeric membranes. The developed approach combines (1) the Flory-Huggins (F-H) description of phase equilibrium thermodynamics, and (2) the Maxwell-Stefan (M-S) diffusion formulation. For compatibility reasons, the M-S equations are reformulated in terms of volume fractions, rather than the more commonly used mole fractions. Using matrix algebra, explicit expressions are derived for calculation of the trans-membrane fluxes and component permeabilities. The accuracy of the developed procedure is demonstrated by comparison with published experimental data on CO2/C2H6 and water/ethanol mixture permeation. (C) 2016 Elsevier Ltd. All rights reserved.