The permeability and selectivity of pure carbon dioxide, methane and its binary mixture at various feed pressure, temperature and composition through non-porous silicone rubber membranes was studied. It was observed that the permeability of pure methane and carbon dioxide increases with pressure, whereas such plots for carbon dioxide become convex towards pressure axis at higher pressures (17 bars) due to reduction in free volume of the polymer. The experimental results showed that for binary mixtures of carbon dioxide and methane, permeability depended not only on the feed gas pressure but also on the molar composition of the feed gas. The permeation flux was found to increase with pressure differences, and the enhancement of the proportion of the carbon dioxide in the feed gas. Experimental results showed that the selectivities estimated from pure gas varied slightly with increase in the feed pressure but reached to a maximum value of 11.4. With 20% CO2 in the feed stream, the selectivity was found to be lower by a factor of two to three times than that of pure components over the whole pressure range. High selectivities were obtained at 80% CO2 in the feed stream. An analytical model expressed in terms of pressure and feed composition was derived from permeability behavior of pure carbon dioxide and methane to predict quantitatively the permeability of binary mixtures. It was indicated that the model could be used to evaluate the separation properties and to choose the optimal feed compositions for the membrane separation systems of carbon dioxide and methane.