We present a model of an elastomeric material whose network microstructure is characterized by a molecular weight distribution (MWD). The MWD is allowed to evolve in time and the evolution is governed by an integro-differential equation that is based on chemo-kinetic mechanisms of eo crosslink degradation and main chain scission. With respect to main chain scission, we differentiate between random and centrally weighted events. We further introduce a particular network free energy function that is a generalization of the eight-chain model and a finite deformation viscoelasticity model. For this combination, we develop closed form solutions to two experimentally imposable strain histories. These results permit the calibration of the MWD evolution model. A sample calibration of the developed formalism is shown against hypothetical "experimental data".