The finite element mathematical models were developed to simulate the solidification andthe elasto-plastic stress of colltinuous casting billet in mold. In the models, a gap-dependent heat trallsfercondition was introduced to modify the average heat flux equation, and the variations of material propertiesas wen as Yield function with temperature and strain rates were considered. The influence of air gap at thebillet corner on the thermal and mechanical behavior of continuous casting billet was investigated...