This paper addresses the problem of locating service facilities on networks vulnerable to disruptions so as to maximize service availability, defined as the capability of the network to provide service when disruption occurs. Most often, demands originating at network nodes are not deterministic. Nevertheless, planners may estimate demand probability distributions based on the estimated impact of the disruptions. Demands for services are modeled in this study as random variables with known probability mass functions. Service availability is measured using, (i) expected amount of service delivered and (ii) average performance of the network. Optimal locations are sought (a) when average demands originate at the nodes and (b) when taking into account all demand scenarios when network disruption occurs. Procedures are presented for both approaches that find single facility locations on general networks or multi facility locations on tree networks. To avoid intractability in two-terminal reliability calculations, the most reliable route policy is adopted. Numerical examples are provided to illustrate the procedures.