We present a comprehensive model to predict the molecular weight distribution (MWD),(1) and branching distribution of low-density polyethylene (IdPE),(2) for free radical polymerization system in a continuous stirred tank reactor (CSTR).(3) The model accounts for branching, by branching moment or pseudo-distributions. The common free radical polymerization reactions including chain scission have been considered in the model. Non-linear or the so-called topological scission has been modeled using approximate fragment length distributions derived from scission, applied to branching topologies. To model the distributions, the Galerkin-FEM method based on the same principles as PREDICI (R) has been applied and implemented in MATLAB (R). The fundamental numerical problem arising from topological scission has been solved. Thus, the model provides more accurate results, allowing a precise comparison to earlier results and to Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.