Whether the particle will be trapped by the solid-liquid interface or not is dependent on its moving behavior ahead of theinterface, so a mathematical model has been developed to investigate the movement of the particle ahead of the solid-liquidinterface. Based on the theory for the boundary layer, the fluid velocity field near the solid-liquid interface was obtained, andthe trajectories of particles were calculated by the equations of motion for particles. In this model, the drag force, the addedmass force, the buoyance force, the gravitational force, the Saffman force and the Basset history force are considered. Theresults show that the behavior of the particle ahead of the solid-liquid interface is affected by the physical property of theparticle and fluid flow. And in the continuous casting process, if it moves in the stream directed upward or downward nearvertical solid-liquid interface or in the horizontal flow under the solid-liquid interface, the particle with the diameter from 5μmto 60 μm can reach the solid-liquid interface. But if it moves in horizontal flow above the solid-liquid interface, only theparticle with the diameter from 5μm to 10μm can reach the solid-liquid interface.