For simulation of thin-wall injection molding, accurate viscosity data measured at shear rates up to 800,000 s(-1) and more are important, but not available in any commercial material database. Such data can be measured on conventional injection molding machines with the help of a rheological mold, which is constructed like a standard injection mold with interchangeable dies. It enables operators to measure viscosity in time on their own machines at practically relevant shear rates (from 10(2) s(-1) to 2 x 10(6) s(-1)). A special feature allows measuring the pressure dependency of viscosity using closed-loop counter pressure control. Experimental data are evaluated taking into account the melt temperature rise due to dissipative heating. 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-filled nanocomposite, 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). Four injection molding dies have been also used to reach apparent shear rates up to 800,000 s(-1). 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.