Unidirectional heat flow is required during directional solidification, so it is very difficult to solidify directionally because of strong side radiation around a water-cold copper crucible. The feasibility of directional solidification with the cold crucible was analyzed by mathematic analysis from electromagnetism, temperature field and heat transfer. Results show that Joule heat is strongest at triple point, and it can counterweigh the side heat dissipation; therefore isotherms approach level near the contact point between the hump and the crucible. Increasing of the electromagnetic force and the degree of superheat of the melt can decrease side radiation of the crucible wall. Consequently it is possible to realize directional solidification with the cold crucible.