Abstract: Traditional methods apply system minimum capacity vectors to calculate the reliability of stochastic-flow network with two separate minimal paths (2SMPs), which needs to store the arc of entire network and the process of removing redundant vectors is complex. In view of this, based on multi-valued decision diagram (MDD) for 2SMPs, we propose a reliability analysis algorithm, called MDD_2SMPs. The main idea of this algorithm is using MDD to reflect the relationship between components status and system status, by defining MDD operators, the path capacity can be obtained without the need for flow distribution. Besides, the constraint pruning strategy is introduced in the process of combination to filter many unnecessary combinations. Furthermore, aiming at the problem of path failure, all paths are converted into MDD variables by using the proposed algorithm MDD_BMPs, resulting a great reduction of the computational complexity. Example analysis shows that the proposed algorithm based on MDD has less calculation burden than traditional methods and can select the network backup paths accurately.