Gear pumps are frequently used for the transport of high viscosity fluids, for instance in the production of tires. In the extrusion process of tire compounds, an external gear pump controls the flow rate of the system. This typically results in a high pressure at the exit of the pump, which is needed to push the material through the die. In this work, the two dimensional flow of a viscous fluid through an external gear pump is numerically studied using the finite element method (FEM). Local mesh refinement based on the respective distance between boundaries is essential to capture the relatively narrow clearances in the pump. The gear pump works against the pressure driven flow, therefore its efficiency is strongly dependent on material and processing parameters. The flow of Newtonian and shear-thinning fluids through the external gear pump is studied for a range of processing conditions. When tracking the residence time of the fluid in the pump using a convection equation, it appears that vortices are present at the inflow causing material to remain in the pump.