This paper reports some results of an ongoing Research Project called RINTC aimed at computing the risk of collapse of buildings conforming to the Italian Seismic Design Code. The project involves different areas of application (reinforced concrete, masonry, steel buildings, etc.) including reinforced concrete (RC) buildings equipped with isolation systems. In particular, this paper focuses on seismic isolation systems based on High Damping Natural Rubber (HDNR) bearings, which are widely employed for buildings and other structures. The aim of the paper is to evaluate the response dispersion due to the uncertainties in the seismic input as well as the variability of the isolation system properties. The study proposes a model to define the p...