The continuous casting process is an example of a complex multi-phase phenomenon coupling turbulent flow, free surface waving, solidification and magnetohydrodynamics forces during the electromagnetic braking. As shown by the authors, the complex topology of the Lorentz force is not limited to damping. Due to the e-current lines closure, the quiescent melt is entrapped into the mean flow, causing the jets flattening and to the formation of the reverse flow zones. Thereby, the application of the magnetic field can cause the undesired instability of the free surface. Base on the developed multi-phase MHD model a comparison of the interface tracking methods was performed: (i) algebraic MULES approach; (ii) a piecewise linear interface calculation (PLIC) method; (iii) the isoAdvector method presented by Rønby. The methods were compared by a wide range of parameters in application to model the free surface behavior between the conductive and dielectric phases for the MHD flows.