Abstract: A two-dimensional mathematical model of solidification and heat transfer for a bloom with the cross section of 425 mm × 320 mm was established, which simulated the growth process of the solidified shell. The model was verified by nail-shooting experiments in the narrow side of the bloom. The solidified shell thickness distribution at any fixed location in the casting direction and the position of the solidification end point were got by the model. It is found that the traditional solidification square root law is not fit for describing the solidification process. A mathematical relationship was regressed between the solidified shell thickness and the square root of solidification time in the center of the wide side. The regression results show that it is approximately linear from the mold meniscus to the secondary cooling zone export, which satisfies the square root law. However, from the secondary cooling zone export to the solidification end point, it is a non-linear relationship, which no longer follows the square root law.