The heat transfer characteristics at the interface between the mold and the casting is one of the major factors for the solidification speed which determines the casting structures. The thermal resistance exists due to air gap formation at the mold/casting interface during the freezing process. In this study one dimensional Stefan problem with the air-gap resistance in the cylindrical mold is considered and the heat transfer characteristics is numerically examined by using the enthalpy method which is convenient in solving the Stefan problem with mushy zone. The present results agreed very well with those of previous papers. The effects of major parameters such as thermal conductivity, heat transfer coefficient of mold, on the thermal characteristics are investigated.