A numerical method for computation of macrosegregation in a solidifying alloy is presented. The formulation relies only on the fundamental conservation laws for mass, momentum, heat and solute, and the thermodynamical relations governing phase change. The entire time-dependent process is simulated, up to complete solidification. The method is applied to the case of an iron-carbon system solidifying in a two-dimensional rectangular mould, cooled from the sides. The thermal and solutal convection that arises during solidification is computed. The evolution of the melt fraction in the mould, and the final distribution of carbon after solidification, is reported.