A transient,two-dimensional,coupled 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 heat flux function,and the variations of material thermal properties,mechanical properties as well as the yield function with temperature were considered.The solidification and shrinkage processes of four round billets and two square billets were simulated by indirect coupled method.Simulation results show that carbon content,pouring temperature,casting speed and shape of billets have distinct influence on the solidification shrinkage of billets.Ideal continuous parabolic tapers were designed and optimized according to the calculated shrinkage curves of billets. A transient, two-dimensional, coupled finite element model was employed to simulate the solidification and shrinkage of continuous casting steels by means of ANSYSTM. The model, a gap-dependent heat transfer condition was introduced to modify the heat flux function, and the variations of material thermal properties, mechanical properties as well as the yield function with temperature were considered. The solidification and shrinkage processes of four round billets and two square billets were simulated by indirect coupled method. Simulation results show that carbon content, pouring temperature, casting speed and shape of billets have distinct influence on the solidification shrinkage of billets. Ideal continuous parabolic tapers were designed and optimized according to the calculated shrinkage curves of billets.