A modified cellular automaton-based method is developed to study the evolution of the solidification grain microstructure during the LENS (TM) rapid fabrication process. The method is coupled with a finite difference-based procedure for computation of the temperature field during both the substrate re-melting/feed-powder injection stage and the solidification stage of the LENS (TM) process. A distribution of the potency of nucleation sites is used to model heterogeneous nucleation both within the melt pool and at the substrate/melt interface. The dendrites are enabled to grow preferentially in the cubic crystallographic directions and the kinetics of dendrite-tips motion is assumed to be controlled by the local undercooling. The method developed enables the establishment of the relationships between the LENS (TM) process parameters (e.g. laser power, laser velocity), and the resulting solidification microstructure in any binary metallic material. The application of the model to Al-7.0 wt.% Si alloys yielded results which are in a generally good agreement with their experimental counterparts,