Molecular dynamics (MD) simulations have been used to study bulk atactic polystyrene (aPS). A united-atom non-bonded potential is calibrated for the aromatic-ring carbons, which, along with previously determined non-bonded functions, results in a good representation of pressure-volume-temperature relations for aPS. Experimental X-ray scattering data for glassy aPS are well reproduced in simulation. Packing features in the glass are discussed in terms of various site-site radial distribution functions. Diffusion coefficients for methane as an example of a small-molecule penetrant are determined as a function of temperature in the range 380-550 K. The values from simulation when extrapolated to room temperature via an Arrhenius plot are found to be consistent with experimental values for the similar gas CO2 at that temperature, thus implying that the glass transition in the matrix has little effect on the diffusion. The temperature behaviour of the diffusion coefficients as well as the detailed jump behaviour of the penetrant indicate that the diffusion mechanism corresponds to hopping from site to site in a solid-like medium over the temperature range studied. The lack of effect of the glass transition on diffusion is rationalized in terms of the mechanism already being hopping in a solid-like medium well above T-g. Diffusion is the slowest in aPS of any of the polymeric matrices studied so far by MD simulation. This correlates well with the fractional free volume found, which is also the lowest yet found in the polymeric matrices.