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This paper proposes an analytical method to investigate the correlation between origin-destination (OD) demands in stochastic transportation network with demand uncertainty. Different from the existing researches, the OD traffic demand is assumed to follow a multivariate probability distribution, which explicitly considers the correlation between OD demands. Under this assumption, the correlation between path flows and correlation between link flows are also deduced using the proposed analytical method. As a result, the multivariate distribution of link flows and path flows can be obtained, which are further applied in a reliability-based traffic assignment problem. The numerical examples indicate that the correlation between OD demands will influence not only the flow patterns but also the total network travel time. Moreover, the ignorance of correlations between OD demands can either underestimate or overestimate the network congestion.