Fiber-reinforced composite materials receive not only a static force but a dynamic force when they are used in practical structures. Especially, the impact response in the direction perpendicular to fibers is the most important, but tardy in research. In this report, first we treat wave reflection and transmission at the interface of different element materials, by using the one-dimensional theory of stress waves. Secondly, those results are applied to some simple models of unidirectional fiber-reinforced composite materials and impact responses in the direction perpendicular to fibers are calculated. Model I and II are composite structures in which two semi-infinite elastic solids are bonded with a thin layer made of a different material. Model III and IV are composed of two and three bonded layers, respectively. These models subjected to impact loading receive a larger tensile stress at the interface than those subjected to static loading, and it is predicted that the tensile fracture at the interface easily occurs.