The purpose of this paper is to develop an efficient algorithm for determining the most vital arcs in a weighted network and implement its algorithm on GIS. The most vital arcs in a weighted network of GIS is that arc whose removal from the network results in the greatest increase in shortest distance between two specified nodes. These studies are well applied to a situation where a logistics or communications network is broken by unexpected accidents. Because a user of the system wants to know which arcs are most vital to him so that he can reinforce them against unexpected accidents. We first present an algorithm to find the most vital arcs in a weighted network, then show that how its algorithm can be applied to a geo-spatial network.