The most vital arc in the maximum flow problem is that arc whose removal results in the greatest reduction in the value of the maximal flow between a source node and a sink node. This paper develops an algorithm to determine such a most vital arc(MVA) in the maximum flow problem. We first define the transformed network corresponding In a given network in order to compute the minimal capacity for each candidate arc. The set of candidate arcs for a MVA consists of the arcs whose flow is at least as greate as the flow over every arc in a minimal cut As a result, we present a method in which the MVA is determined more easily by computing the minimal capacity in the transformed network. The proposed method is demonstrated by numerical example.