Solidification of an aqueous ammonium chloride (NH4Cl-H2O) solution inside a two-dimensional cavity is numerically investigated using a continuum mixture mathematical model. The mushy region where solid and liquid phases co-exist is considered a non-Newtonian fluid below a critical solid fraction, and a porous medium thereafter. This critical solid fraction is chosen as that corresponding to the coherency point, where a solid skeleton begins to form. The numerical results show that the solidification of a hypereutectic NH4Cl-H2O solution is mainly characterized by the rejection of solute at the mushy region and double diffusive convection induced by the opposing solutal and thermal buoyancy forces. The mathematical model agrees satisfactorily with the available experimental and numerical data.