Abstract: On the basis of the rapid growth model for dendrite and eutectic and the criterion of the highest temperature for interface growth, an interface response function (IRF) of eutectic alloys during rapid equiaxed solidification was established. With the IRF, competitive growth between the primary and eutectic phases of Al-Si alloys was investigated and a microstructure selection map of Al-Si alloys during non-equilibrium solidification was constructed. The calculation results show a good agreement with those of atomization experiments, indicating that the IRF model can be used to predict satisfactorily the microstructure selection and evolution of Al-Si alloys.