The multiple-impact phenomena usually exist in many engineering structural system and the calculation of impact force is a key problem. The present study is aimed at the calculation method of the impact force of the longitudinal multiple-impact problem. The transient wave response approach was presented to investigate the history of the multiple impact forces based on the theory of transient wave propagation. The wave effect was sufficiently considered. The transient wave response approach could avoid solving the impact force from the strongly nonlinear equation coupled of impact force with impact motions. The flexible system of two flexible rods with longitudinal multiple impacts was investigated accurately in numerical example. The higher the initial impact velocity is, the bigger the impact forces will be. The impact forces in the previous third impact processes increase slowly with the impact number. The phenomena of "sub-impact" can be captured. The present method provides an effective method for reference to further investigate the multiple-impact problem in the more complex flexibility systems and the longtime dynamic behavior.