It is important for many industrial processes to design new materials with improved selective permeability properties. Besides diffusion, the molecule's solubility contributes largely to the overall permeation process. This study presents a method to calculate solubility coefficients of gases such as O-2, H2O (vapor), N-2, and CO2 in polymeric matrices from simulation methods (Molecular Dynamics and Monte Carlo) using first principle predictions. The generation and equilibration (annealing) of five polymer models (polypropylene, polyvinyl alcohol, polyvinyl dichloride, polyvinyl chloride-trifluoroethylene, and polyethylene terephtalate) are extensively described. For each polymer, the average density and Hansen solubilities over a set of ten samples compare well with experimental data. For polyethylene terephtalate, the average properties between a small (n = 10) and a large (n = 100) set are compared. Boltzmann averages and probability density distributions of binding and strain energies indicate that the smaller set is biased in sampling configurations with higher energies. However, the sample with the lowest cohesive energy density from the smaller set is representative of the average of the larger set. Density-wise, low molecular weight polymers tend to have on average lower densities. Infinite molecular weight samples do however provide a very good representation of the experimental density. Solubility constants calculated with two ensembles (grand canonical and Henry's constant) are equivalent within 20%. For each polymer sample, the solubility constant is then calculated using the faster (10x) Henry's constant ensemble (HCE) from 150 ps of NPT dynamics of the polymer matrix. The influence of various factors (bad contact fraction, number of iterations) on the accuracy of Henry's constant is discussed. To validate the calculations against experimental results, the solubilities of nitrogen and carbon dioxide in polypropylene are examined over a range of temperatures between 250 and 650 K. The magnitudes of the calculated solubilities agree well with experimental results, and the trends with temperature are predicted correctly. The HCE method is used to predict the solubility constants at 298 K of water vapor and oxygen. The water vapor solubilities follow more closely the experimental trend of permeabilities, both ranging over 4 orders of magnitude. For oxygen, the calculated values do not follow entirely the experimental trend of permeabilities, most probably because at this temperature some of the polymers are in the glassy regime and thus are diffusion dominated. Our study also concludes large confidence limits are associated with the calculated Henry's constants. By investigating several factors (terminal ends of the polymer chains, void distribution, etc.), we conclude that the large confidence limits are intimately related to the polymer's conformational changes caused by thermal fluctuations and have to be regardedat least at microscaleas a characteristic of each polymer and the nature of its interaction with the solute. Reducing the mobility of the polymer matrix as well as controlling the distribution of the free (occupiable) volume would act as mechanisms toward lowering both the gas solubility and the diffusion coefficients.