A two-dimensional (2D) cellular automaton (CA)-finite element (FE) model developed for the prediction of grain structure formation during solidification processes is presented. While the FE method solves the macroscopic conservation equations for heat and mass transfers, the CA method is used at a mesoscopic scale to simulate the growth of a mushy zone domain. The limit between this mushy zone domain and the undercooled liquid melt in which it develops defines the envelope of a single grain. A verification is first performed to check that the CAFE model retrieves the solution of a purely FE simulation for a vanishing undercooling of the growth front. Since the present 2D CAFE model is relevant with respect to the solidification experiment developed by Yin and Koster [H. Yin, J. N. Koster, J. Crystal Growth 205 (1999) 590; H. Yin, J. N. Koster, J. Alloy Compd. 352 (2003) 197], comparison is then performed. In particular, the position of the growth front is considered as a time sequence. The effect of the growth undercooling is clearly revealed. The kinetics of the growth front used in the model assumes the development of a rough interfacial dendrite-like morphology. This assumption is discussed considering the value of the normalized entropy of fusion of gallium.