Abstract: Impact problems for elastic bodies usually use Signorini conditions to represent the contact conditions. These conditions have lead to a number of questions regarding first existence of solutions, and second, conservation of energy. We can get a glimpse of the effect of viscosity and the type of contact region by looking at a number of simple examples for which existence can be shown without viscosity. Proofs of conservation of energy have proved elusive in general, although results have been obtained in special situations. A framework for proving conservation of energy will be set up which shows the crucial role of the regularity of the solution and the contact forces. This is work with Jeongho Ahn (Yonsei University).