During solidification of a melt or solution, a constitutively supercooled mushy layer is often formed in front of the phase transition boundary. This process leads to the nucleation and growth mechanisms of newly born solid particles within a two-phase domain that is responsible for the crystal structures and properties. The process of solidification with a supercooled two-phase domain is analytically described on the basis of directional and bulk crystallization models. Such characteristics as crystal-size distribution function, constitutional supercooling, solid fraction and radial density distribution function of solids in the mushy layer are found.