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In this study, the leakage of a non-Newtonian fluid, i.e. silicone oil, in a generic gap was numerically investigated. A CFD tool is used to determine the relationship between leakage flow, gap length and pressure difference. The investigated fluid is viscoelastic and its properties are modelled by a Maxwell equation. The Maxwell model can be used to precisely define the phenomenon of stress relaxation. Moreover, a comparison of the viscosity of measured data with simplified models shows that the Maxwell model is best suited for viscosity prediction. Furthermore, simulation results showed that at low pressures, leakage is reduced by decreasing the gap angle. However, this effect changes with increasing viscosity and relaxation time of the molecule. To determine the pressure drop, the Bagley plot is used. The results confirmed that as the shear rate increases, the elastic pressure drop values increase. In addition, the leakage flow increases with an increasing slenderness ratio.