An analytical model is developed for the prediction of the shape of dendritic grain envelopes during solidification of a metallic alloy in a Bridgman configuration (i.e. constant thermal gradient and cooling rate). The assumptions built into the model allow a direct comparison of the results with those obtained from a previously developed cellular automaton-finite element (CAFE) model. After this comparison, the CAFE model is applied to the study of the extension of a single grain into an open region of liquid after passing a re-entrant corner. The simulation results are compared with experimental observations made on a directionally solidified succinonitrile-acetone alloy. Good agreement is found for the shape of the grain envelopes when varying the orientation of the primary dendrites with respect to the thermal gradient direction, the velocity of the isotherms or the thermal gradient.