The morphological instability analysis is carried out for non-stationary solidification of a binary melt. We demonstrate that both the morphological and dynamic neutral stability curves coincide. The neutral stability curve for morphological perturbations does not intersect the self-similar branch of solutions for solidification, that is, the morphological instability does not cause the mushy zone origination whereas the constitutional supercooling arising ahead of the stable planar front solidifying in self-similar manner is a reasonable criterion for the mushy region incipience. The theory under consideration is in a good agreement with experimental and numerical studies carried out by Huppert and Worster. (C) 2003 Elsevier Ltd. All rights reserved.