A numerical method is presented for the calculation of the three-dimensional flow and separation efficiency for particles with low concentrations in a hydrocyclone. Multi-block curvilinear grids in the frame of a cylindrical coordnate system are used to represent accurately the hydrocyclone geometry. Turbulence is represented by a modified k - epsilon model which adds a curvature correction term with a single empirical constant in the dissipation equation. Both three- and two-dimensional axisymmetric computations are carried out and are compared with experimental data. It is shown that the standard k - epsilon model can produce large errors which result in incorrect predictions of the flow patterns. The three-dimensional calculations using the modified k - epsilon model produce results in good agreement with experimental data. The two-dimensional axisymmetric calculations can predict approximate flow patterns, but are inadequate to predict the separation efficiency of hydrocyclones. To analyse the separation efficiency, a three-dimensional model, as developed in the present study, is required.