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A new method for reliability analysis of stochastic flow networks is proposed. Nodes as well as branches can have limited capacities and can fail. The method builds a branching tree. The tree-nodes are the disjoint terms of a symbolic reliability expression. The paper shows how to find the probability function and mean of the network performance. The method is both simple and effective. The minimal paths or cutsets are not needed explicitly. On a computer the memory effort is very low Â¿ it increases only quadratically with the number of failing elements. The method can be modified reasonably for other reliability problems.