Based on covalent bond scission force estimates from single molecule experiments and a statistical analysis of the instantaneous segmental tension (ST) distribution in bead-rod chains, a new algorithm has been developed for the simulation of flow-induced polymer chain scission. This algorithm overcomes the nonphysical time-step dependence inherent in stochastic chain scission simulations that employ instantaneous ST-based criteria to identify scission events. This is accomplished by the use of a normalized ST profile that is independent of the elongation rate E for asymptotically large values of the Weissenberg number, defined as the ratio of the longest relaxation time of the chain to 1/E. The algorithm is employed to study chain scission in steady and transient elongational flows as well as the effect of hydrodynamic interactions on chain scission in steady elongational flow. Simulation results for steady elongational flow reproduce the experimentally observed scaling law for the critical elongation rate E-c alpha M-w(-2) where M-w denotes the molecular weight. Moreover, for E approximate to E-c, the chains unravel via a coil-to-stretch configurational transition. Since ST attains its maximum at the midpoint of the chain, the midpoint scission hypothesis (MSH) is valid. This leads to a relatively narrow distribution of daughter chains. However, for E >> E-c sufficiently large ST could develop in the elongated portions of partially coiled chains. Consequently, chain scission could occur farther from the midpoint. MSH is not valid under such conditions, and the resulting distribution of daughter chains is relatively broad. Hydrodynamic interactions are shown to slow down chain unraveling leading to an increase in E-c with the scaling E-c alpha M-w(-1.7). The effect of polymer residence time on E-c is examined by investigating scission of polymer chains that traverse the centerline of a regularized contraction flow. It is found that the scaling relationship between E-c and M-w remains the same as that for steady elongational flow given that the residence time exceeds 5% of the longest relaxation time of the chain. This result suggests that the inverse proportionality of E-c to M-w observed experimentally in contraction flow might be due to preshearing effects. Finally, the effect of loading rate on scission probability is discussed in the context of an extended thermally activated barrier to scission model. (c) 2007 The Society of Rheology.