The process of freeze coating of a polymeric melt on an axially moving continuous cylinder is studied numerically by a finite-difference method, taking into account heat convection from the melt to the freeze coat and spatial variation of the cylinder temperature. The solid-liquid interface location is immobilized in the finite-difference analysis of the problem by transforming the system of equations governing the behavior of the freeze coat and the cylinder temperature into a dimensionless space. Various controlling parameters of the system are identified and their effects on the growth-and-decay behavior of the freeze coat are determined. Also determined are the maximum freeze-coat thickness and the corresponding axial location, based on which criteria for selection of the optimum freeze-coating operation conditions are established. The accuracy of the computational scheme is demonstrated by comparing the numerical results with the similarity solutions that are valid at small dimensionless axial locations.