Numerous numerical models for simulating solidification of metals on a microscopic scale have been proposed in the past, among them are most importantly the phase-field method and models based on cellular automata. Especially the latter have up to now only been suitable for the consideration of binary alloying systems. Since industrial alloys are usually constituted of multicomponent alloys, the possibility of applying cellular automata is rather limited. With the aim of enhancing this modelling technique, a new, modified approach is proposed in the course of this thesis. The model uses the physical fundamentals of solute and heat diffusion in two dimensions as a basis for determining the solidification progress. The implementation of the effects of several alloying elements on the solidification velocity is achieved by a functional extrapolation of the concentration gradient towards the interface. The model shows the typical behaviour of dendritic solidification, such as parabolic tip and secondary dendrite arm formation as well as selection of preferably aligned columnar dendrites. A validation of the model is performed by comparing it with predictions of well-established dependencies in the literature, and by evaluating morphological parameters and comparing them to experimentally determined values. Dendritic growth in multicomponent (C-Si-Mn-P-S) steels is studied for different initial concentrations and cooling rates. It is possible to reproduce columnar as well as equiaxed solidification morphologies and to derive conclusions on the complex interactions between solute diffusion, heat extraction and solidification progress in multicomponent alloys on a microscopic scale.