Having taken the solid network movement in the two-phase zone into consideration, this paper develops the original local solute redistribution equation. The additional term divV’(s) in the new equation is dependent on the history of an effective stress sigma’ acting upon the solid network. The solidifying isotherm advances quickly and there is not enough time to make the solid network compressible at large cooling rates. With decreasing cooling rate, movement of the isotherm is gradually slowed and there is enough time to make the network deformed. It is suggested that the compressibility due to the normal stress may produce "channel space" filled by unstable flow under the conditions of small cooling rate during solidification. The calculated results have demonstrated that the back-flow toward the centerline increases when the stress is considered.