Natural disasters often lead to regional failures which can fail down network nodes and links co-located in a large geographical area. It will be beneficial to improve the resilience of a network by assessing its vulnerability under regional failures. In this paper, we propose the concept of α-critical-distance to evaluate the importance of a network node in the geographical space with a given failure impact ratio α. Theoretical analysis and a polynomial time algorithm to find the minimal α-critical-distance of a network are presented. Using real Internet topology data, we conduct experiments to compute the minimal α-critical-distances for different networks. The computational results demonstrate the differences of vulnerability of different networks. We also find that with the same impact ratio α, the studied topologies have smaller α-critical-distances when the network performance is measured by network efficiency than giant component size.