An impact on the ground surface may represent several phenomena, such as a crash of an airplane or an explosion or the passage of a train. In order to analyze and design structures and equipment to resist such a type of shocks, the response spectra for an impact on the ground must be given. We investigated the half-space motions due to impact using the finite element method. We performed extensive parametric analyses to define a suitable finite element model and arrive at displacement time histories and response spectra at varying distances from the impact point. The principal scope of our study has been to derive response spectra which: (a) provide insight and illustrate in detail the half-space response to an impact load, (b) can be readily used for the analysis of structures resting on a ground subjected to an impact and (c) are a new family of results for the impact problem and can serve as reference for future research.