This work presents a numerical study of liquid-gas-solid flow in classifying hydrocyclones (CHs). In the numerical model, the turbulent flow of a liquid-gas-solid mixture is modelled using the Reynolds stress model. The interface between the liquid and air core, and the particle flow are both modelled using the mixture multiphase model under different conditions. The flow features are examined in terms of flow field, pressure drop, amount of water split to underflow, and separation efficiency. The approach is first verified by comparing the measured and calculated results. Then, it is used to investigate the effects of feed solids concentration and its fluctuation. The results show that when feed solids concentration is increased, the separation efficiency decreases while the cut size increases; the inlet pressure initially decreases to a minimum and then increases, and the amount of water split to underflow firstly increases to a maximum and then decreases. It is also shown that the air core, solid mass flowrates on the underflow and overflow, and inlet pressure drop fluctuate corresponding to feed solids fluctuation. However, the fluctuation only affects the average CH separation efficiency slightly.