Monte Carlo and molecular dynamics simulations were performed to calculate solubility, S, and diffusion, D, coefficients of oxygen and water in polyethylene, and to obtain a molecular-level understanding of the diffusion mechanism. The permeation coefficient, P, was calculated from the product of S and D. The AMBER force field, which yields the correct polymer densities under the conditions studied, was used for the simulations, and it was observed that the results were not sensitive to the inclusion of atomic charges in the force field. The simulated S for oxygen and water are higher and lower than experimental data, respectively. The calculated diffusion coefficients are in good agreement with experimental data. Possible reasons for the discrepancy in the simulated and experimental solubilities, which results in discrepancies in the permeation coefficients, are discussed. The diffusion of both penetrants occurs mainly by large amplitude, infrequent jumps of the molecules through the polymer matrix.