In this paper, a comprehensive three dimensional mathematical model is built to investigate the effect of electromagnetic stirring (EMS) on continuous casting process of copper round billet. The electromagnetic field is simulated by ANSYS software and the thermal-flow field is simulated by FLUENT software. The coupling between electromagnetic field and thermal-flow field is implemented by user-defined subroutines. The simulation results have good agreement with the experiment ones. The results show that electromagnetic frequency and current intensity have significant influence on the fluid velocity, temperature gradient and sump depth. The optimum current intensity and frequency are found to be 40A and 10Hz respectively.