At present, there is a lack of research on the influence of different dynamic constitutive models of steel and concrete on the dynamic mechanical properties of concrete-filled steel tubular (CFST) columns under lateral impact. In this paper, A comprehensive numerical study on the effects of different dynamic constitutive models of steel and concrete on the lateral impact response of CFST columns was conducted. The dynamic constitutive models of steel and concrete with different strengths were divided into four categories, namely, normal-strength steel, high-strength steel, normal-strength concrete and high-strength concrete. The established finite element model of CFST columns considering the progressive damage degradation of steel as well as the compressive and tensile damage factors of concrete was verified against published experimental data. Based on the verified FE model, the effects of different dynamic constitutive models of steel and concrete on the impact response of circular CFST columns were analyzed. The analyzed results show that the different dynamic constitutive models of steel have different effects on the impact force and mid-span time-history deflection curves of CFST columns. The analysis result, ignoring the effect of concrete strain rate, is in good agreement with the CEB-FIP model considering the effect of steel strain rate. This is because the largest proportion of the impact energy of CFST members is mainly assimilated by the outer steel tube.