Abstract: By considering the elastic-plastic deformation behavior of multiple contacts and the conditions of multiple impacts and multiple separations and by using the finite difference method, the MCIS method was presented to investigate the impact problem of a simply supported beam struck horizontally by a round-nosed rigid mass. 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 considerable impact impulse or even more than ones of the first impact zone. Hence, the other impact zones have significant influence on the impact responses of the beam. It is found as well that the other impacts might have considerable impact kinetic energy dissipation totally or even more than ones of the first impact. It implies that the multiple impacts are of an important role upon the impact physical behavior of the beam. The numerical investigations also show that for the light rigid mass, the first impact course will cause more kinetic energy dissipation, and for the weight rigid mass, the following multiple impact courses will cause more kinetic energy dissipation.