The paper presents a simplified theoretical analysis of liquid solidification on cold flat and cylindrical walls with special emphasis on the role of the contact layer that forms on them. The theory is based on analytical calculations adapted from the kinetic theory of gases. The results show the dependence of the thickness of the contact layer on the thickness of the solidified layer. In addition, the influence of the contact layer on the solidification process has been shown. The development of the thickness of the solidified layer and the influence of the contact layer has been determined for selected liquid and solidification parameters. (C) 2015 Elsevier Ltd. All rights reserved.