Diffusion coefficients of He, O-2, N-2, CO2, and CH4 at 300 K in four silicone polymers, namely, poly(dimethylsiloxane) (PDMS), poly(propylmethylsiloxane), poly((trifluoropropyl)methylsiloxane), and poly(phenylmethylsiloxane), have been estimated by molecular dynamics (MD) simulations. The estimated diffusion coefficients decrease with increasing size of the polymer side chains and of the penetrant molecules, as was also found experimentally. The estimated diffusion coefficient for He in PDMS is consistent with its experimental value. The values of the estimated diffusion coefficients for the other gas/silicone systems considered in this study are within +/- 40-60% of the corresponding experimental values. The MD simulations revealed two types of motions of the penetrant molecules : (1) "jumps" from one cavity in a silicone matrix to another, and (2) "oscillating motions" inside cavities. The lengths of the jumps are of the order of 8-15 Angstrom, whereas the oscillating motions are of the order of less than or equal to 5 Angstrom. The total timeframe for the execution of a jump is about 5 ps (5 x 10(-12) s). The number of jumps and the average length of a jump of a penetrant molecule inside a silicone matrix decrease as the size of the molecule and of the polymer side chain increase. Some problems associated with the estimation of gas diffusion coefficients in polymers by MD simulations are also discussed.