Two-dimension unsteady heat transfer model was applied to obtain the surface temperature and the shell thickness of continuous casting slabs during the process of solidification. On the basis of which, the mathematical model of strain at the interface of solid and liquid steel was set up. Through which, the strain in the solidifying shell under normal and abnormal operation conditions was gained. The results indicate that the strain is small under the normal operation conditions and the internal crack never happens.However, when the variation of the roll gap is above 2 mm, the strain caused by which is greater than that caused by bulging. Furthermore, the total strain exceeds the critical one and the internal crack is the result. So it is of great importance to maintain the fine state of continuous casting machine to avoid the appearance of internal crack.