When the melt or solution solidifies a constitutionally supercooled mushy layer is frequently formed ahead of the phase transition boundary. This leads to nucleation and growth mechanisms of newly born solid particles within a mush. The latter is responsible for the structures and properties appearing in the crystal. The process of solidification with a supercooled mushy layer is analytically described on the basis of two joint theories of directional and bulk crystallization. Such characteristics as the constitutional supercooling, the solid fraction and the radial density distribution function of solid particles in a mushy layer are found. The complex structure of the non-equilibrium mushy layer is completely recognized. (c) 2006 Elsevier Ltd. All rights reserved.