By assuming an elastic-perfectly plastic constitutive relation for the material and employing a model which consists of four compressible elastic-plastic bars connected by four elastic-plastic "hinges" of finite length, the dynamic behaviour of an inertia-sensitive impact energy-absorbing structure (previously called a Type II structure) under impact is analysed in detail. By taking account of the complicated deformation history involving loading, unloading and reversed loading, the large deformation process is traced completely and the variation of the "impact force" with time or with the vertical displacement is determined. In particular, the peak load is determined on the basis of elastic-plastic material behaviour and the consideration of inertia effects. The analysis presented indicates that the dynamic behaviour of the structure considered significantly differs from the quasi-static behaviour of the same structure even when the effect of strain-rate on the material properties is excluded. Therefore, inertia would appear to be the dominant effect in this sort of impact problems.