In this thesis, a theoretical description of mass transport through membranes used in pervaporation separation processes has been investigated for both dense polymeric membranes and mixed matrix membranes (MMMs). Regarding the dense polymeric membranes, the Maxwell-Stefan model was extended to consider the effect of the operating temperature and membrane swelling on the mass transport of species within the membrane. The model was applied semi-empirically to predict the membrane properties and separation performance of a commercial Polydimethylsiloxane (PDMS) membrane used in the pervaporation separation of butanol from binary aqueous solutions. It was observed that the extended Maxwell-Stefan model has an average error of 10.5 % for the prediction of partial permeate fluxes of species compared to roughly 22% for the average prediction error of the Maxwell-Stefan model. Moreover, the parameters of the model were used to estimate the sorption properties and diffusion coefficients of components through the PDMS membrane at different butanol feed concentrations and operating temperatures. The estimated values of the sorption properties were observed to be in agreement with the literature experimental data for transport properties of butanol and water in silicone membranes while an exact comparison for the diffusion coefficient was not possible due to large fluctuations in literature values. With respect to the MMMs, a new model was developed by combining a one-directional transport Resistance-Based (RB) model with the Finite Difference (FD) method to derive an analytical model for the prediction of three-directional (3D) effective permeability of species within ideal mixed matrix membranes. The main novelty of the proposed model is to avoid the long convergence time of the FD method while the three-directional (3D) mass transport is still considered for the simulation. The model was validated using experimental pervaporation data for the separation of butanol from aqueous solutions using Polydimethylsiloxane (PDMS)/activated carbon nanoparticles membranes and using data from the literature for gas separation application with MMMs. Accurate predictions were obtained with high coefficient of regression (R2) between the calculated and experimental values for both applications.