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The general aim of this work is to build a model of solidification that includes all pertinent elementary phenomena, which may contribute to the segregation in the sub-surface region of continuously cast metal. This paper presents a first attempt to take into account simultaneously: the solidification shrinkage, the thermal contraction of both the liquid and solid phases, the thermomechanical deformation of the mushy zone, and the undercooling at the growth front.Mathematical expressions of segregation rates occurring during solidification with spongy deformation of an alloyed mushy zone have been derived from classical mass balance equations. The main result is a mathematical expression for the local macrosegregation rate. This expression is combined with a numerical one-dimensional model of the heat flow previously developed for the study of directional solidification of an undercooled mushy zone using an Eulerian frame of reference. In addition to inverse segregation close to the mold, segregation induced by deformation and growth undercooling of the columnar growth front are predicted. Application to the solidification of the skin of steel cast products agrees qualitatively well with experimental observations.