A stress jump, defined as the instantaneous gain or loss of stress on startup or cessation of a deformation, has been predicted by various models and has relatively recently been experimentally observed. In this paper, the internal viscosity idea is incorporated into the transient network model. Via appropriate approximations, we obtain a closed constitutive equation where the total stress equals the sum of an elastic contribution and a viscous contribution. As the latter is rate dependent, the model predicts a stress jump and we consider data on shear flow in this contribution. We successfully compare the model predictions with the stress jump measurements of Liang and Mackay [C.H. Liang, M.E. Mackay, J. Rheol. 37 (1993) 149]. The model yields good quantitative predictions of the steady, transient and dynamic material functions.