Continuous casting is considered to be the major growth area in the U.S. steel industry. It combines the casting and hot rolling operations, saving energy and handling costs. The heat transfer and solidification phenomena need to be better understood to perfect the design of the casting machines and prevent formation of defects in the cast metal. The purpose of this work is to generate the knowledge required. The approach is to extend previous modeling efforts, using ANSYS software for heat transfer calculations, along with material property data generated in the laboratories of Inland Steel Corporation. A model will be developed to simulate the continuous casting process. The model will calculate the temperature distributions in the casting mold and the solidifying steel, using an assumed set of heat transfer coefficients. The temperature solution will be used to compute the distorted shapes of the mold and billet. From the distorted shapes, a new set of heat transfer coefficients will be determined for the temperature problem. This procedure will continue until a consistent set of temperature and thermal stress fields is obtained. The work will be extended, using a super-computer, from two-dimensional to three-dimensional cases. Phase changes, convection, and temperature-dependent elastic-plastic effects will be considered.