Abstract: Some rules of computer numerical simulation for the directional solidification with steep temperature gradient have been found out.In order to improve the accuracy in the numerical simulation for the directional solidification with steep temperature gradient, the effect ofin heat transfer equation on the computational results is discussed and how to treat the heat of fusion, thermal property of the casting/mould interface and initial conditions etc. are analyzed.Two computation methods-finite difference and finite element methods-are used for the same test ingot with the identical initial conditions, boundary conditions and thermophysical parameters. The advantages and shortcomings of the both methods are compared.