The aim of this study was to develop a model that predicts the gas solubility and the sorption and desorption kinetics in polymer granulates over large temperature and pressure intervals. Besides the part predicting the solubility and diffusivity, the model involves the simultaneous solution of the diffusion equation and the heat equation in three dimensions using a finite element method (FEM). When the temperature- and pressure-dependent solubility of a specific polymer/gas combination is not known, an improved version of the non-equilibrium lattice fluid model (NELF) is used to predict the solubility. The improvement of the NELF model includes the use of Hansen's solubility parameters, and it uses pressure-volume-temperature (PVT) data from two new empirical models, which accurately estimate polymer densities over a wide range of temperatures and pressures. The new solubility model predicted the solubility-pressure data of N-2 in poly(ethyl methacrylate) and N-2 and CH4 in polycarbonate (PC) at pressures below 4.5 MPa, without using any adjustable interaction parameters. The model was used to predict the solubility of N-2 in poly(ether-ether-ketone) (PEEK) and PC at a very high pressure (67 MPa). Experimental N-2 solubility data were obtained with a specially built reactor yielding high pressure and temperature. For PEEK, it was possible to predict the very high pressure solubility using a gas-polymer interaction parameter obtained from data taken at low pressures In addition, a new free-volume-based diffusivity model requiring no adjustable interaction parameters was developed, and it successfully predicted the desorption kinetics of N-2 from PEEK and PC.