The object of this paper is the presentation of a theoretical solidification model of heat-conducting liquid metal flowing near of a cold plate. The problem of the unsteady behaviour both of the frozen metal layer and of the cold plate is studied analytically, Influence of the contact layer between the frozen layer and the cold plate on the solidification process is also studied. The results in the form of the analytical formula,and the graphs are presented and compared with the other results. (C) 2003 Elsevier Science Ltd. All rights reserved.