The design of gear pumps and motors is focused on more efficient units which are possible to achieve using advanced numerical simulation techniques. The flow that appears inside the gear pump is very complex, despite the simple design of the pump itself. The identification of fluid flow phenomena in areas inside the pump, considering the entire range of operating parameters, is a major challenge. This paper presents the results of simulation studies of leakages in axial and radial gaps in an external gear pump carried out for different gap shapes and sizes, as well as various operating parameters. To investigate the processes that affect pump efficiency and visualize the fluid flow phenomena during the pump’s operation, a CFD model was built. It allows for a detailed analysis of the impact of the gears’ eccentricity on leakages and pressure build-up on the circumference. Performed simulations made it possible to indicate the relationship between leakages resulting from the axial and radial gap, which has not been presented so far. To verify the CFD model, experimental investigations on the volumetric efficiency of the external gear pump were carried out. Good convergence of results was obtained; therefore, the presented CFD model is a universal tool in the study of flow inside external gear pumps.