Abstarct: In this thesis, the maximum flow problem in fuzzy networks has been studied. In the maximum flow problem, the goal of a maximum amount of flow from the source vertex to the sink vertex in a network respect to the limitation that no arc can not exceed the capacity of the arc is included. In the first chapter, the problem of maximum flow in networks is described in the definitive exxpression of Ford and Fulkerson algorithm. The second chapter is dedicated to define fuzzy networks and operations of fuzzy numbers are triangular and trapezoidal. The third chapter is represented an algorithm for solving the maximum flow problem in fuzzy networks. The fourth chapter is described of solving the fuzzy linear programming method.