I present a model study of brittle fracture of polymers. I show that the relation nu=nu( F) between the crack-tip velocity nu and the driving force F exhibit discontinuous transitions and hysteresis. For short polymers, at the onset of crack propagation the polymer chains separate by pulling out the molecular chains, while a discontinuous transition to a new state of rapid crack motion occurs at higher driving force, where the polymer chains break. In contrast to earlier atomistic studies of crack motion involving brittle materials such as silicon, for short polymers we find (at zero temperature) that the onset of crack motion is continuous, i.e., the crack-tip velocity nu increases continuously from zero when F is increased above the critical value F (c) necessary for starting crack motion. The difference is attributed to inertia, which is less important during pull-out of the molecular chains, than in models where the crack motion involves breaking strong short-ranged bonds. I also present a detailed study of the polymer chain pull-out process.