A numerical analysis on the freeze coating process of a non-isothermal finite dimensional plate with a binary alloy is performed to investigate the growth and decay behavior of the solid and the mushy layer of the freeze coat and a complete procedure to calculate the process is obtained in this study. The continuously varying solid and mushy layers are immobilized by a coordinate transform and the resulting governing differential equations are solved by a finite difference technique. To account for the latent heat release and property change during solidification, proper phase change models are adopted. And the convection in the liquid melt is modeled as an appropriate heat transfer boundary condition at the liquid/mushy interface. The present results are compared with analytic solutions derived for the freeze coating of infinite dimensional plates and the discrepancy is found to be less than 0.5 percent in relative magnitude for all simulation cases. In addition the conservation of thermal energy is checked. The results show that the freeze coat grows proportional to the 1.2 square of axial position as predicted by analytic solutions ar first. But after the short period of initial growth, the growth rate of the freeze coat gradually decreases and finally the freeze coat starts to decay. The effects of various non-dimensional processing parameters on the behavior of freeze coat are also investigated.