Fast cooling and solidification of high-temperature droplets of opaque melt is considered. The problem parameters correspond to interaction of core melt with ambient water in hypothetical severe accident in some industrial nuclear reactors. A recently suggested approximation for transient temperature profile in the particle during solidification is employed. This approach is combined with an analytical solution for quasi-steady stress-strain state of growing solid crust layer. A computational analysis showed that the resulting tensile stress on the particle surface is maximal at a certain position of solidification front. The latter is considered to be a reason of mechanical breakage of corium particles at time preceding this stress maximum. The results obtained are in qualitative agreement with recently reported observations of some fragments of thick-wall hollow spherical particles in laboratory experiments. (C) 2008 Elsevier Ltd. All rights reserved.