In this study, the lattice fluid (LF) and non-equilibrium lattice fluid (NELF) theories combined with the modified Fick's law and free volume theory were employed to develop mass transfer models for the prediction of gas sorption and permeation in glassy and rubbery membranes in a wide range of temperature and pressure. The finite element method using COMSOL multi-physics software was used to solve the governing transport equations. The gas sorption into the glassy membranes shows a non-equilibrium behavior in spite of the rubbery membranes in which the gas sorption is in the equilibrium state. The results indicated that the membranes with higher fractional free volume show higher solubility and diffusion coefficients. The proposed model can predict satisfactory the gas solubility and permeability in the glassy and rubbery membranes and determine the influence of operating pressure and temperature on the transport properties of the membranes without need of any adjustable parameters. (C) 2017 Elsevier Ltd. All rights reserved.