Molecular dynamics simulations have been carried out in order to examine the mechanism of diffusion of small penetrants in amorphous polymer membranes. Diffusion processes of methane, water, and ethanol in poly(dimethylsiloxane) (PDMS) and in polyethylene (PE) were investigated. Pure liquid water and ethanol were also simulated. The insertion probabilities P(R) of hard-sphere atoms of radius R into the polymers and the liquids were calculated. The free volume fraction, P(0), of PDMS is large and the insertion probability of a finite size atom into PDMS is widely distributed compared with the other polymers and liquids. Simulations of 5 ns were performed for PDMS and in PE with a penetrant species, methane. The diffusion of methane in the polymer matrix exhibits anomalous (non-Einstein) behavior for time scales of land 0.3 ns in PDMS and PE, respectively. Aggregates of water and ethanol are found to be formed in PDMS. Diffusion coefficients of water and ethanol in PDMS are reduced by more than 1 order of magnitude due to the aggregation. The calculated diffusion coefficients of the nonaggregated penetrants in PDMS and in the pure liquids agree well with the experimental values.