Abstract: Combining the theory of traveling magnetic field with the Navier-Strokes equation for fluid motion, a mathematical model was developed for the 3-D flow field in a cylindrical container to prepare metallic materials under the action of traveling magnetic field. In addition, a new model was introduced to compute the electromagnetic force. It was found through comparison that the modeling results is in accord with the experimental results made by Gerbeth, thus verifying the reliability of the model developed and relevant computation program. When the aspect ratio decreases, the flow field structure in container has no change, i.e., the two symmetric vortices remain unchanged, but their shapes change to rectangular from elliptic. When the electromagnetic force increases, the axial velocity curve changes to steeple parabola from flat one and the stronger the electromagnetic force, the shorter the distance between wave apex and container bottom surface.