A three-dimension mathematical model has been developed to describe the magnetic field, fluid flow and inclusion transport in a continuous caster with electromagnetic brake (EMBR). According to the model, all the governing equations can be expressed as a general differential equation, so a general numerical method was developed to solve these equations. The numerical results agree well with the experimental result. In the continuous caster, the inclusion distributions have 'M' shape under the nozzle and W shape at the exit, which come from the centrifugal effect and the collision and aggregation among inclusions. The three-dimensional static magnetic field can effectively damp local flows and affect the inclusion transport in a continuous caster. If EMBR is installed under the nozzle, it can promote the inclusion removal and the inclusion 'M' distribution disappears.