We have developed a simple bead-spring model, intended to mimic the internal dynamics of individual polymer chains in the region of the glass transition temperature. Entanglement constraints on the chains are approximated by "sliplinks." We model the chain dynamics using a dynamic Monte Carlo scheme, with a hop acceptance criterion based on the traversal of high energy barriers. We use this to address the recent experiments of Hine et al., which investigated the effects of melt processing on stress-strain behavior. Polystyrene samples were stretched, annealed at constant length for various times, then either subjected to shrinkage tests or further stress-strain tests. Our model reproduces, at a qualitative level, the observations of Hine et al. It indicates that whilst the initial (weak) strain hardening involves deformation of chain subunits smaller than the entanglement length, the transition to stronger strain hardening involves the "pulling tight" of a small fraction of chain strands trapped in between entanglements. The insights gained suggest a route towards development of molecular-based constitutive models for strain hardening in the glassy state, and specifically the effect of melt processing. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 920-938, 2011