Using capillary dies having different diameters, D, and length-to-diameter L/D ratios, a full rheological characterization has been carried out for a polypropylene melt, and the experimental data have been fitted both with a viscous model (Cross) and a viscoelastic one (the Kaye - Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko or K-BKZ/PSM model). Particular emphasis has been given on the pressure-dependence of viscosity. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios.