The definition of network medians is extended to the case where travel times on network links are random variables with known discrete probability distributions. Under a particular set of assumptions, it is shown that the well known “facilities at nodes” theorems of Hakimi and of Levy can be extended to such stochastic networks. The concepts are further extended to the case of stochastic oriented networks. A particular set of applications, as well as mathematical programming formulations of the problem, are also discussed briefly.