The process of solidification of metal is accompanied by liquid-solid change and known as Stefan`s heat conduction problem on the moving boundary. In this study the temperature distribution in ingot and metallic mould during casting was analyzed by the two dimensional heat conduction theory. The transient temperature distribution was numerically calculated using a finite element method on the nodal point of mesh screen representing ingot and mould cross section. The theory was applied on the casting of aluminum(purity ; 99%) in flat ingot mould of GC25. The analysis will make it possible to calculate an optimum mould shape of which temperature gradient becomes minimum.