In the last decades, the study of volcanic hazard in a probabilistic framework has become one of the most rapidly developing topics in volcanology, but also in decision making and education, in particular for risk mitigation issues. A number of tools (either methodological or numerical) have been developed to help scientists apply quantitative methods in different volcanic settings. Of paramount importance is then quantifying uncertainties (both aleatory, which reflects the intrinsic natural variability of eruptive processes, and epistemic uncertainty, due to our limited knowledge on such processes).In this scenario, numerical models can reproduce volcanic processes under different conditions and their impacts over a wide range of spatial and temporal scales, hence assisting a more focused use of sound statistical methods to assess volcanic hazards (e.g. sector collapses, lahars, pyroclastic flows, debris flows, lava flows, ballistic dispersal, gas dispersal). This session aims to collect contributions from numerical modeling to the evaluation of volcanic hazards through probabilistic techniques in order to highlight their applications in long and short-term PVHA. Since civil protection and researches have been focused on the public’s understanding of volcanic hazards, particular attention should be paid to education programs. Therefore, we also encourage contributions that discuss about applications of PVHA for education and civil protection purposes.