A numerical model of binary alloy crystallization, based on the cellular automaton technique, is presented. The model allows to follow the
crystallization front movement and to generate the images of evolution of the dendritic structures during the solidification of a binary
alloy. The mathematic description of the model takes into account the proceeding thermal, diffusive, and surface phenomena. There are
presented the results of numerical simulations concerning the multi-dendritic growth of solid phase along with the accompanying changes
in the alloying element concentration field during the solidification of Al + 5% wt. Mg alloy. The model structure of the solidified casting
was achieved and compared with the actual structure of a die casting. The dendrite interaction was studied with respect to its influence on
the generation and growth of the primary and secondary dendrite arms and on the evolution of solute segregation both in the liquid and in
the solid state during the crystallization of the examined alloy. The morphology of a single, free-growing dendritic crystal was also
modelled. The performed investigations and analyses allowed to state e.g. that the developed numerical model correctly describes the
actual evolution of the dendritic structure under the non-equilibrium conditions and provides for obtaining the qualitatively correct results
of simulation of the crystallization process.