The molecular network theory due to Yamamoto has been considered, and the effect of modeling the network segments as non‐Gaussian chains has been investigated. By using a non‐Gaussian free energy expression for the entanglement creation function and a constant breakage function, one finds that the resulting material functions will depend on the number of subunits in the network segments. For short segments, an initial increase with shear rate occurs in the viscosity, which can be attributed to the increased energy of dissipation during their deformation by the applied flow field. Introduction of a slip coefficient to remove the affine deformation assumption results in shear thinning behavior, which becomes more pronounced for long polymer segments. Depending on the network segment length and the slip coefficient, it is shown that our choice of entanglement creation and destruction functions leads to the results of Lodge's theory for affine non‐Gaussian chains on one hand, and to Fuller and Leal's predictions for non‐affine Gaussian chains on the other.