Two- and three-dimensional (3D) Cellular Automaton (CA) algorithms are proposed for modelling the growth of dendritic grains from the liquid phase. These CA growth algorithms are validated for simple thermal situations by comparing the predicted grain shapes with those deduced from analytical models. The insight obtained by the 3D approach is demonstrated by studying the extension of a single dendritic grain in a squared platform (i.e. at a section change of a casting mould) under various conditions. In particular, the effects of crystallographic orientation, thermal gradient, velocity of the isotherms and growth kinetics are shown. This 3D CA growth algorithm, coupled with finite element heat flow calculations, will become a major tool for the prediction of dendritic grain structures in solidification processes.