An external gear pump is a relatively simple and inexpensive pump, that is used in a variety of production systems. Numerous works have studied the external gear pump using numerical simulations; however, typically low‐viscosity fluids and turbulent flow conditions are considered. Previous work of the authors focused on predicting the output fluctuation and the volumetric efficiency of an external gear pump processing high‐viscosity fluids using a 2D representation. For certain conditions, backflow through all clearances could occur, resulting in a drop in volumetric efficiency. This calls for a full 3D model. Furthermore, high residence time zones are observed in the inflow channel of the pump. The 3D shape of these zones is still unknown. The aim of this work is to investigate the effect of the axial clearances on the performance of the external gear pump. A 3D mesh is generated by extruding the 2D mesh in the third direction, resulting in prism elements. This reduces the required number of elements and therewith makes the simulations computationally feasible. Introducing the axial clearances results in a lower efficiency compared to the 2D simulations. With particle tracking, the high residence time zones in the inflow channel are visualized in the 3D simulations. In extrusion processes, external gear pumps are frequently used to transport all kinds of fluids. 3D simulations are performed using the finite element method to investigate the relative importance of the radial and axial clearances in the pump. Particle tracking reveals zones with infinite residence time.