Abstract: In the dynamic impact response analysis of the structure， the dynamic amplification factor （DAF） is usually used to sim? plify the calculation of the dynamic response of the structure. However， the size of DAF in engineering structures is still controver? sial. In order to solve this problem， the analytical expression of DAF of multi-degree-of-freedom system （MDOF） is derived in this paper， and the precondition of DAF greater than 2.0 is analyzed. The accuracy of the analytical expression is verified by the sin? gle-degree-of-freedom （SDOF） and MDOF example models， and the reason why the DAF of the MDOF is greater than 2.0 is ex? plained. Finally， based on the DAF analytical method proposed in this paper， the DAF distribution law of beam string under cable breaking impact is analyzed. The analysis results show that when the contribution of a first-order modal shape is opposite to the stat? ic response， the DAF of the beam string may be greater than 2.0. Even for the damping system， the DAF of the beam string may be greater than 2.0.