Rheological properties of polymer melts are often described with a linear model, the two-parameter power-law model in industrial applications, while the real polymer melts behave more or less nonlinearly, particularly in the low shear rate regions. In a lot of real flows, such as the simple pipe flow, there is even a zero shear rate region. Therefore, the adequacy of this linear approximation has to be examined. In this paper, the polymer melt flow in a pipe is studied using the nonlinear three-parameter Powell model. Numerical results are presented in several graphs, which can be used in engineering calculations. A comparison with the test data has been given. The restrictions of using the power-law model and the impact in handling the experimental data are discussed.