This paper considers the growing of a solid layer on a sheet that moves through a liquid and which is kept at a temperature below freezing. The convection in the liquid is fully taken into account. It is found that the thickness of the layer is proportional to the square root of the distance from the point where the sheet enters the body of liquid. The main difficulty lies in determining the factor of proportionality in this relationship. Asymptotic expressions are derived for this factor in the case where latent heat is much greater than sensible heat. Also presented are approximate solutions valid for very small (liquid metals) and very large (polymers) values of the Prandtl number.