In order to facilitate the numerical calculations of the phase boundaries in large industrial floating zone silicon crystal growth with the needle-eye technique, the chain of improved mathematical models is developed. The phase boundaries are solved in a partly transient way and the modelling improvements cover the open melting front, the inner triple point and the free melt surface. The view factors model is applied for the radiative heat transfer. The electromagnetic field is calculated with account of a multiple-slit inductor. (C) 2003 Elsevier Science B.V. All rights reserved.