The main aim of this paper is to study the maximum flow problem when t
he underlying associated structure is not well defined and must be mod
eled as a fuzzy graph. However, to deal with the problem it is necessa
ry to develop several well known concepts from classical theory, in th
e fuzzy graph context, such as flow, network, and admissible flow. The
above maximum flow problem is formulated and solved by using algorith
ms previously developed by the authors.