Beyond the definition and measurement of energy poverty, which have mainly attracted research interest over the last decades, attention has recently begun to turn to a broader notion of energy vulnerability. So far, this has mostly been approached on a theoretical base, suggesting the incorporation of broader socio-economic aspects into the energy poverty framework. However, the quantitative measurement of energy vulnerability is still an unexplored field of research. In this paper, the "Vulnerability Index" is developed, which, based on stochastic analysis, quantifies the vulnerability of a population to the energy poverty ratio, compared to a reference population. Moreover, Sensitivity Analysis quantifies the particular contribution of various parameters to the problem, by determining their weighting factors. As case study, the vulnerability of Greek mountainous regions with respect to the country level was studied. The results showed that households living in mountainous regions are more vulnerable versus those of the whole country, at 89.7%. It was also found that energy policy should focus on raising incomes of mountainous population and, afterwards, on energy saving measures and reduction of heating cost in mountains. The methodology suggested can address social inequalities of vulnerable population groups, in terms of energy poverty. (C) 2018 Elsevier B.V. All rights reserved.