In order to investigate more suitable sample configurations for obtaining radially larger and more homogeneous compound semiconductor crystals, a two-dimensional model of the traveling liquidus-zone method is introduced. From numerical results of the model, it is found that inhomogeneity increases with the thermal conductivity of a crucible wall. This is mainly attributed to the heat flow slanted towards the crucible wall near an interface. The numerical results show, however, that the low thermal conductivity of the crucible does not sufficiently reduce the inhomogeneity, which is caused by the slanted heat flow. We also investigate the influence of a seed crystal. It is found that a seed crystal with large thermal conductivity is far more effective to improve the homogeneity. (C) 2011 Elsevier B.V. All rights reserved.