A stochastic model based on the coupling of the cellular automaton technique with the finite volume method was developed to simulate the formation of solidification grain structures in the squeeze casting of an Al-4.5mass%Cu alloy. The present model was also applied to predict the CET (columnar-to-equiaxed transition). The interfacial heat transfer coefficients between the casting and the die were evaluated as a function of time using an inverse problem method. Solidification sequences in squeeze casting were simulated using the calculated interfacial heat transfer coefficients. The effects of casting process variables on the CET and the solidification grain structures in squeeze casting of an Al-4.5mass%Cu alloy were investigated. The predicted solidification grain structures were in good agreement with those obtained experimentally. It was found that the CET can be predicted using the concept of the interface velocity at the solidification front.