Research in heat transfer and solidification commonly involves experimentation and mathematical modeling with associated numerical analysis and computation. Inverse problems in heat transfer are part of this paradigm. During the solidification of metal casting, an interfacial heat transfer resistance exists at the boundary between the casting and the mold, and this heat transfer resistance usually varies with time. In the case of the squeeze casting the contact heat transfer resistance is decreased by pressure and ideal contact is almost accomplished. In the present work, heat transfer coefficient, which is inverse value of the heat transfer resistance, was used for convenience. A numerical technique, Non-Linear Estimation has been adopted for calculation of the casting/mold interfacial heat transfer coefficient during the squeeze casting process. In this method, the measured temperature data from experiment were used. The computational results were applied to the analysis of heat transfer and solidification.