The efficiency of material flow systems in terms of optimal network flow and minimum cost flow has always been an important design and operational goal in material handling and distribution system. In this research, an attempt was made to develop a new algorithm and the model to solve a stochastic material flow network with bidirectional and uncertain flows. A stochastic material flow network with bidirectional flows can be considered from a finite set with unknown demand probabilities of each node. This problem can be formulated as a special case of a two-stage linear programming problem which can be converted into an equivalent linear program. To find the optimal solution of proposed stochastic material flow network, some terminologies and algorithms together with theories are developed based on the partitioning and subgradient techniques. A computer program applying the proposed method was developed and was applied to various problems.