By using Linearization method in little time interval, from the heat conduition equation with the 1st-order phasetransformations, the foundation equations of Finite Elememts in solidifications of Metals is established in the paper. The numerical analog on symetric problem in solidification of a grayiron in sandform is obtained by means of triangular element, and the results tallies the corresponding test well.

In this paper, Norsette Method is used to solve the non-steady heat conduction problem. This method prevents the "oscillation" of numerical solution effectively.