The paper is devoted to the mathematical modeling of problems of growth of CdZnTe (CZT) crystals at high-pressure inert atmosphere by a crystal growth method during which an axial heat flux close to the phase interface is applied (AHP-method) [V. Golyshev, M. Gonik, Patent of RF # 180085415, 1990]. The AHP-method is a modification of the Bridgman method with an additional heater submerged into the melt. The aim of the work is to understand the reasons of inhomogeneities in CZT crystals grown by the AHP under conditions of week melt flow of melt. Therefore, test case problems are solved by numerical modeling to understand the influence of thermal conditions in the furnace on the shape of the melt/crystal (m/c) interface and on the homogeneity of the composition of CZT crystals. The results of numerical modeling are compared with experimental data. It is shown that the change of the shape of the m/c interface during CZT crystal growth is caused by a drastic change of the thermal resistance of the whole system. The changing interface shape is the main reason for the inhomogeneity of the CZT crystals grown by the ARP method. (c) 2007 Elsevier B.V. All rights reserved.