In an earlier paper, a nonaffine network model of polymer melts was presented in which the rotation caused by shearing as well as the extension of the test strand are hindered by interactions with the network itself. In that work, it was shown that such a strand motion leads to qualitatively correct steady shear and elongational material properties, even though the strand disentanglement rate was constant and the strand force law was linear. These simplifications were accepted in order to emphasize the effects of the strand motion on material properties. In this paper, however, we show that these idealizations cause the model to fail in the start-up of shearing flow because no overshoot is seen in the shear stress growth function. To address this failure, the finitely extensible nonlinear elastic (FENE) network model is introduced in which the FENE force law replaces the Hookean force law used in the earlier finitely extensible network strand (FENS) model. Also, a nonlinear expression for the kinetics of strand disentanglement replaces the assumption of a constant rate of disentanglement. Material properties for the FENE network model are generated by stochastic simulation. The simulation results show that these modifications produce overshoot in the shear stress growth function and result in a more consistent description of finite network strand extensibility.