In this paper we present a method forcomputing the eddy currents in induction meltingprocesses for non-ferrous alloys. We take intoconsideration the situation when only the crucible ismoving, inside the coils. This fact makes differentialcomputation methods to be hard to apply, because isnecessary to generate a new mesh and a new systemmatrix for every for every new position of the cruciblerelated to the coils. Integral methods cancel thisdrawback because the mesh is generated only for thedomains with eddy currents. For integral methods, themesh and the inductance matrix remain unchangedduring the movement of the crucible; only the free termsof the equation system will change.