A two dimensional analysis of the solidification phenomena has been simulated by IAD (Implicit Alternating Direction)method for L-shaped castings with external chills. The effect of chills has been studied with the variation of chill size, shape, and their materials, and also with the variation of the pouring temperature. Three kinds of cross-sectional shapes of chills such as triangle, square, and L-shape were chosen, and graphite, cast iron, and copper for their materials. It has been shown by the computation that the hot spot at the junction of L-shaped castings can not be removed by external chills, and that the distance between the inner corner and the hot spot on the line of symmetry, as well as the solidification time of castings depend only on VHC (Volumetric Heat Capacity).