In order to design optimal polymer membranes it is important to have a molecular level understanding of penetrant transport in such membranes. As such, molecular dynamics simulation was employed to study the diffusion and solubility of gas molecules in polypropylene (PP), poly(propylmethylsiloxane) (PPMS) and poly (4-methyl- 2-pentyne) (PMP). After the structures of PP, PPMS and PMP were established and relaxed, the average amplitudes of the oscillation of the main and branch chains of PP, PPMS and PMP were evaluated with a proposed analysis method; in addition the cavity size distributions of PP, PPMS and PMP were determined. PPMS has the largest average cavity size and accessible cavity fraction for penetrants, followed by PMP and PP, which has the smallest. The logarithm plot of mean-squared displacements (MSDs) versus time for the transport of methane in the three polymers revealed three regimes, namely the ballistic, the subdiffusive and the Fickian diffusive regimes. The ballistic regime of PMP is longer than that of PP and shorter than that of PPMS, because the average cavity size and accessible cavity fraction of PMP are larger than that of PP and smaller than that of PPMS and the penetrants have less space in PP and more space in PPMS to move freely than they do in PMP before they hit any matrix units. Statistical tests showed that the random walk on a fractal (RWF) model was the most appropriate model to explain the subdiffusion phenomena. The subdiffusive regime is induced by the trap of penetrants in cavities before they get the chances to jump from cavities to cavities nearby. Next the diffusivities of methane and n-butane were estimated from the plot of MSDs versus time for the penetrant transport in the Fickian diffusive regime. The diffusivities of penetrants are much smaller in PP than they are in PPMS and PMP and these values are larger in PPMS than they are in PMP. With both unbiased and biased Widom insertion methods, the solubility coefficients K of gas molecules in the polymers were calculated, though biased Widom insertion method has significantly faster calculation speed. PPMS has the largest solubilities of methane and nbutane, followed by PMP and PP, which has the smallest. Though the permeabilities of both methane and nbutane in PPMS are larger than the corresponding values in PMP, the selectivity of n-butane over methane in PPMS is lower than that in PMP. The research results may be employed in membrane design.