A 2-D finite point meshless model was used to simulate the heat transfer and solidification of steel in continuous casting molds to illustrate its use in metallurgy. The latent heat of the pure metal was treated using the temperature recovery method and the latent heat of the alloy was treated using an apparent heat capacity method. The model was validated by calculating the classical Stefan moving boundary problem. Analysis of the solid shell growth and temperature distribution of a billet in a mold shows that the solution by the finite point meshless model is quite reasonable, which indicates that the model has potential in metallurgical engineering applications.