The results of a numerical simulation of a non-Newtonian flow of a shear thinning fluid inside a hydrocyclone are presented. The fluids used were carboxy-methylcellulose polymer solutions whose rheological properties were described using a power law shear-rate dependence. This system is a model analogue for drilling fluids. An axisymmetrical, laminar swirl flow was analysed by solving a set of conservation equations in which the air core radius was explicitly included, employing a surface-tension force balance equation. The results predicted a distinct difference in velocity distribution within the hydrocyclone between a shear-thinning fluid compared to a simple Newtonian fluid. The predicted non-Newtonian fluid velocity agreed well with independent flow and velocity measurements obtained from Laser Doppler Anemometry. The thickness of the vortex finder is shown to have a significant effect on the flow pattern in the hydrocyclone, and this is likely to affect the classification efficiency. This result has important implications for the design and selection of hydrocyclones for handling non-Newtonian mixtures.