This paper discusses shear viscosity measurements of polymer melts by the capillary rheometer. Particular emphasis is placed on investigating the effects of viscous heating and pressure dependence of viscosity in capillary flows. The capillary flow problem is addressed by means of numerical simulation using the finite element method to solve the equations of continuity, momentum and energy along with the viscosity model that accounts for the dependence on shear rate, temperature and pressure. Simulations clearly reveal that viscous heating and pressure dependence of viscosity can have a considerable impact on capillary rheometer experiments. On the other hand, as far as the pressure drop over the capillary is concerned, it is possible that these two contributing factors compensate for each other. Selected experimental data from the capillary rheometer are also presented and discussed in connection with the simulated results.