Impact between structures of bridge sections can play a major, unexpected role in seismic structural damage. Linear and non-linear models are developed to analyze structural impact and response of two single-degree-of-freedom structures, representing adjacent buildings or bridge sections. The analyses presented assess probability of impact, displacement change due to impact, and the probability of increased displacement due to impact. These are assessed over a matrix of structural periods for each degree-offreedom, different impact coefficients of restitution, and a probabilistically scaled suite of earthquake events. Linear versus non-linear effects are assessed using a Ramberg-Osgood non-linear model for column inelasticity. The normalized distance, or gap-ratio (GR), defined as a percentage of the summed spectral displacements, is used to create probabilistic design requirements.