The purpose of this paper is to develop a method of paramatric analysis that can be applied to an optimal solution of a maximum flow problem. We first define the transformed network corresponding to a given network. In such a network, we conduct paramatric analysis by determining changes in the optimal solution precipitated by changes in the capacity as the arc capacity varies from 0 to infinite. By this method we can easily calculate not only the characteristic region where the given optimal solution remains unchanged, but also the characteristic region where the value of the maximal flow gradually increases or decreases. The proposed method is demonstrated by numerical example.