AbstractComputer based numerical modelling of solidification is being increasingly used in an effort to develop and improve casting processes, a long term goal of this work being the prediction of microstructural features such as grain shape, size, and dendrite arm spacings throughout a casting. In a numerical heat flow model this can be achieved only through the inclusion of the kinetics of nucleation and dendrite growth. In the present paper strategies for including columnar and equiaxed solidification kinetics into a finite element model are reviewed. A detailed model for columnar solidification is then presented together with results obtained from calculations on an Al–5 wt-%Cu alloy and a multicomponent nickel based superalloy. It is shown that the inclusion of a dendrite tip undercooling is important, particularly in systems having a low Stefan number. Furthermore, the thermal histories in the superalloy can only be accurately calculated if an experimentally determined solid fraction versus temperature relationship is employed. A model for equiaxed solidification is also discussed and results obtained for an Al–5 wt-%Cu alloy outlined. In particular, the effects of heat transfer coefficient, heterogeneous nucleation site density, and nucleation undercooling on the grain size variation along a one dimensional casting have been examined. Finally, it is shown that grain sizes predicted by the present finite element model agree reasonably well with those of a previous numerical model for an Al–7 wt-%Si alloy.MST/1468