A new formulation of non-affine motion for the network model is proposed and its applications are presented in this manuscript. The major improvement is that a finite elongational viscosity is predicted for finite elongational rates contrary to the infinite elongational viscosities existing at some elongational rates predicted by previous network models. Comparisons with experimental data of the shear viscosity normal stress coefficient and elongational viscosity are given, in terms of the same set of model parameters. Model predictions for the stress growth are also shown.