In order to describe the transient stress growth for polymer melts, the empirical model proposed by Seo for the viscosity of steady-state flow is combined with a phenomenological viscoelastic model of a differential type (the White-Metzner model) along the lines proposed by Souvaliotis and Beris. The relaxation time is taken as a function of the invariant of the stress tenser (hence that of the configuration tensor) rather than that of the rate of the deformation tensor. Numerical results show a good correlation with experimental data. The model predictions approach steady-state values at long times after the startup. The nonlinear form of the model correlates very well with the experimental data over many decades of the deformation rate, both in shearing and elongational deformations. The proposed model is a simple one that can also describe the overshoot in the transient stress growth. (C) 2003 Wiley Periodicals, Inc.