Most often networks provide some critical service in the form of flow from service facilities to customers. Network components (nodes and edges) are vulnerable to intentional or unplanned disruptions, which may lead to path destruction or even disconnectedness between service facilities and customers. This paper introduces the use of a new modeling framework to accurately define service survivability measures on existing networks that are vulnerable to disruptions, and the definition of network performance metrics. Service survivability is understood as the ratio of how much service is available when disruption occurs over the total requested service. Service availability depends on the capability of the network to establish connectivity between facilities and customers so that service may be delivered. This paper focuses on the location of facilities on existing networks so that service survivability is maximized. Examples are the location of servers or databases on computer networks, control systems on telecommunication networks, or critical information on information infrastructures or social networks. Efficient procedures are introduced that avoid the intractability of the traditional two-terminal reliability calculations.