The sorption of gases (CO2, N-2, CH4, O-2) and vapors of different nature (n-butane, n-pentane, i-pentane, n-hexane, n-heptane, methanol, ethanol, 1-propanol, 1-butanol, water, chloroform, toluene, 1,4-dioxane, tetrahydrofurane) in films of a polymer of intrinsic microporosity (PIM-1) was studied at room temperature and various pressures. For the first time, the solubility properties of PIM are studied with a rigorous macroscopic model based on the Lattice Fluid (LF) theory; the LF parameters, not available for PIM-1, were obtained from independent gas sorption data at low pressure. The solubility of gases and water vapor follows the typical concave trend of dense glassy polymers and is described accurately by the Non Equilibrium Lattice Fluid (NELF) model, given the dry polymer density value and a slight adjustment of the binary parameter k(ij). The organic vapor solubility isotherm in PIM-1 can reach very high values and even exhibit a positive concavity at high penetrant contents, that is typical of sorption in rubbery phases. Such portion of the solubility isotherm was thus modeled with the equilibrium LF Equation of State (EoS) and one adjustable parameter k(ij), while at lower activities the sorption was described with the same value of k(ij) and the NELF model. The value of PIM-1 density in the swollen glassy state required by the NELF model is estimated with an a priori scheme, based on pure penetrant liquid volume. The present work shows that, despite its peculiar microscopic structure, the solubility of PIM-1 can be estimated successfully with the same thermodynamic tools used for dense homogeneous phases and a limited number of parameters. (C) 2013 Elsevier B.V. All rights reserved.