Transient two-dimensional model of bismuth germanium oxide (EGO) crystal growth by the heat exchanger method has been developed. The moving boundary problems for the melt/solid interface location, the temperature field in the whole calculation domain and the flow held in the melt were solved by the two mapping rule method, which enabled the simulation of the melt/solid interface, changing from hemispherical to planar shape. The maximum deflection of the interface was observed when the melt/solid interface is at the corner of crucible. The effects of the various growth parameters were studied on the interface shape, the temperature profile and the stream function using this model. As the excess heating temperature was increased, the maximum deflection of the interface decreased. The heal exchanger temperature hardly affects the maximum deflection of the melt/solid interface. The maximum deflection of the melt/solid interface is not very sensitive to the value of the thermal conductivity of the melt of EGO.