A three-dimensional mathematical model is developed to study coupled turbulent flow, heat, solute transport, and solidification in a slab continuous caster with electromagnetic brake. Based oil the analogy analysis, all the governing equations can be expressed as a general differential equation and be solved by a general numerical method. Numerical results show that a small corner-vortex appears near the free surface due to the interaction between the moving solidified shell and the upward flow. Influenced by the fluid flow, the temperature and Solute distribution can also be divided into the upper and lower recirculation zones but the distribution of carbon concentration is opposite to that of temperature. The three-dimensional magnetic field can effectively damp the local flow and affect heat and solute transfer in the mold.