A previous continuum model proposed and recently modified by the authors for describing the heat, mass and momentum transport phenomena in dendrite solidification process of alloy castings was further extended to the solidification cases in an arbitrary electromagnetic (EM)-fields. The extended continuum model and a FEM/FDM joint solution technique were successfully applied to the numerical simulations of directional solidification transport processes in blade-like castings of Pseudo-binary ln718 base-4.85 wt.%Nb and Al-4.5 wt.%Cu alloys under a static or harmonic EM-field of different strengths/frequencies. The computational results demonstrate the availability of the present continuum modeling to treat in EM-STP problem, and also reveal that the volume-contraction-driven liquid feeding flow is much more difficult to be suppressed than the buoyancy-induced by means of applying a static magnetic field. (c) 2005 Elsevier Ltd. All rights reserved.