In this work a comprehensive mathematical framework is developed for modeling gel effect in branched polymer systems with application in the solution polymerization of vinyl acetate. This model is based On Sound principles such as the free-volume theory for polymer chains diffusion. The model predictions for monomer conversion and number- and weight-average molecular weights were found to be in good agreement with published data in the literature. Moreover, the joint molecular-weight distribution-long chain branching distribution is calculated by direct numerical integration of a large system of nonlinear ordinary integral-differential equations describing the mass conservation of macromolecular species in a batch reactor. This allows studying the effect of process conditions such as initiator and solvent concentration oil the product quality. It is believed that this work might contribute to a more rational design of polymerization reactors. (C) 2008 Wiley Periodicals, Inc. J Appl Polym Sci 111: 2171-2185, 2009