When an aqueous solution is brought into contact with a subcooled solid surface, an intermediate stage of ice crystallization is found between the surface nucleation and the growth of ice layer in the normal direction to the solid surface. During this period, ice is formed in thin films spreading along the solid surface until it is completely covered. This process can be found in the process of freeze concentration of aqueous solutions, where ice is formed and removed to concentrate the solutions. The growth rate of ice films in this period is controlled by the heat conduction from the ice into the solid surface. A mathematical model that describes the ice film growth kinetics is presented in this paper, which is expressed using the Modified Bessel Functions. The temperature distribution in the solid slab underneath the growing front of the ice films is derived from the model, and the growth rates of ice films on different solid surfaces are predicted using a numerical method. (C) 2004 Elsevier B.V. All rights reserved.