The finite element model was employed to simulate the solidification and shrinkage of continuous casting steels by means of ANSYSTM. In the model

a gap-dependent heat transfer condition was introduced to modify the function of heat flux

and the variations of material thermal properties

mechanical properties as well yield function with temperature were considered. The solidification and shrinkage processing of four round billets and two square billets provided by enterprise were simulated by indirect coupled method. According to the shrinkage curves of billets

the continuous parabolic tapers for mould were designed.