In order to consider a phase selection in a ternary eutectic system, analytical expressions for three-phase planar eutectic growth have been derived, assuming the geometries as regular, rod+hexagon and semi-regular types. Irrespective of geometries the relations that the undercooling is proportional to the square root of the growth rate of the interface and that the eutectic spacing is inversely proportional to the square root of the growth rate have been given. The parameters used in these growth models are expressed by the physical properties of materials. The predicted structure type and the eutectic spacing are consistent with the reported experimental results.