Induction heating of a molten steel in a channel enhances inclusion removal though its purpose is heating. Thus, the optimum operating condition have not been clarified until now. In this study, theoretical analysis and numerical calculation of the inclusion behavior under the imposition of A.C. magnetic field using simple 2D model have been investigated. The rising velocity of the inclusion gradually increases as it approaches to the upper surface because the dominant driving force in the center area of the molten steel is buoyancy force and that in the upper region is a pinch force. Approximate mathematical expressions of the inclusion trajectory have been derived under the consideration of these dominant force. And removal time of the inclusion has been also theoretically derived. The shielding parameter in the range of 5 - 10 is the optimum condition to minimize the inclusion removal time, because the pinch force is weak in the case of small shielding parameter and the electromagnetic force dominant region is limited only in the vicinity of the metal surface in the case of large shielding parameter. The optimum shielding parameter relates channel size with frequency. Increase in magnitude of the magnetic flux density is another method to decrease the inclusion removal time. The pinch force in the vicinity of the channel wall overcome a force by turbulence and Saffman force under a certain condition which can be realized in industry, thus the inclusion reaches the channel wall.