This paper develops two techniques to analyse the performance of a stochastic-flow network (SFN) model, considering correlated failures. The first approach utilizes a correlated binomial distribution to characterize the failure behavior of the physical lines and routers internal to the individual edges and nodes in the network. The second employs a simulation technique, which can characterize correlated failures between every pair of physical lines and routers in the different edges and nodes comprising the network. Both approaches quantify the probability that a given amount of data can be sent from a source to a sink through this network. This probability that the network satisfies a specified level of demand is referred to as the SFN reliability. The techniques are demonstrated in the context of two case studies, including the Taiwan Academic Network, the backbone of the national computer network connecting all educational institutions in Taiwan. Experimental results demonstrate that correlation can produce a significantly negative impact on reliability, especially when there is a high level of network demand. The proposed approaches, thus, capture the influence of correlation on SFN reliability, offering methods to quantify the utility of reducing correlation.