Abstract: The impact problem of a simply supported beam with variable cross-section struck horizontally by a round-nosed rigid mass is investigated by considering the local deformation behavior of multiple elastic-plastic contacts induced by multiple impacts and multiple separations. A local elastic-plastic contact deformation model is applied and extended for multiple elastic-plastic impact problems. The finite difference method is used to solve dynamic equations. The numerical simulations show that such a horizontal strike is indeed a complicated process of multiple elastic-plastic impacts. There are usually more than two impact zones in which each of them consists of complicated multiple sub-impacts. It is found that the other impact zones might occupy a considerable impact impulse totally comparing to the first impact zone. Hence, the other impact zones have a significant influence on the dynamic response of the beam. It is found as well that the other impacts might make the mass loss considerable kinetic energy totally comparing to the first impact. It implies that the multiple impacts are of an important role upon the impact physical behavior of the beam. In addition, the numerical results show that the variations of the beam’s cross-section will make the impact zones contract or stretch and make the second impact zone take place late or early.