Numerical simulation of the solidification of a modified (Al–Cu) aluminum melt in a cylindrical crucible is performed. The model used describes thermodynamic processes, heterogeneous nucleation, and solidification of α and β components of the melt. A crystalline phase nucleates at the surface of spherical particles upon cooling of the melts below the liquidus temperature that changes in accordance with the concentration of dissolved alloying component. The relation between the supercooling and size of nuclei formed at the surface of nanosized particles is demonstrated. During cooling of the melt from the liquidus temperature to the eutectic temperature, the α component of the melt solidifies; during subsequent cooling, the eutectic solidification of the β component takes place. The nucleation conditions, solidification rate, and solidification time were found to differ substantially within the melt. The reliability of the suggested model is confirmed by comparison of numerical computation results with physical experiment data.