Road networks are vulnerable to natural disasters such as floods, earthquakes and forest fires which can adversely affect the travel on the network that remains intact after an event. However, not all road links equally affect the travel conditions in a given network; typically some links are more critical to the network functioning than the others. It is noted that the majority of the existing indices designed to measure vulnerability offer a good measure of network-wide accessibility in sparse regional networks, but they rarely consider the extent of serviceability of critical links in dense urban road networks. This paper describes a number of vulnerability indices from the literature, applies them to the case of urban network of York and discusses the results. It proposes a new vulnerability index considering the serviceability of road links and illustrates its computation. Finally, this paper uses the results of the new vulnerability index and outlines a traffic diversion plan in the event of flooding in York using traffic network modelling techniques combined with Geographic Information Systems (GIS) application.