The present work is dedicated to explain the development of a computational model for simulating the grain structure formed in a squared billet produced by continuous casting. During steel solidification, three different grain structures are formed as a function of the heat removal conditions. The solidification times previously calculated using a finite difference method were used as input data in order to simulate dynamically the evolution of the grain formation. Computational routines for grouping, counting and classifying have been programmed to evidence the influence of the solidification speed on the grain morphology resulted. Criterions based on solidification speed and time on mushy are used to establish the transitions zones between chill, columnar and equiaxed grains. Routines to simulate grain nucleation and growth based on chaos theory have been included to create a graphical cellular automaton on the computer screen to animate the grain structure formation.