Molecular dynamics (MD) simulations of bulk atactic polystyrene have been performed for chains up to 320 monomer units in a temperature range from 100 to 600 K and in a broad pressure range from 0.1 to 1000 MPa. The MD-determined specific volume vs temperature curves are in a good agreement with experimental PVT data at different values of applied pressure, but the measured glass-transition temperature, T-g, is displaced to somewhat higher temperature than the longer time experimental value. Local translational mobility has been investigated by measuring the mean-square translational displacements of monomers as a function of time. The long-time asymptotic slope of these dependencies is close to 0.6 at T > T-g, showing diffusive behavior. The cage effect, when local translational motions are essentially frozen in the glassy state, has been studied. The characteristic time of cage release does not depend on molecular weight, but the duration of the crossover to the diffusive regime increases almost linearly with increasing chain molecular weight, for both the backbone monomers and phenyl side groups.