In this paper, we present a novel approach based on a rubber band technique to solve the " maximum flow" problem for a single-source, single-sink directed graph implemented on the Microsoft Azure cloud platform. The problem of finding the maximum possible flow for a given graph is a classic network optimization problem that arises in several real life circumstances. Having proposed several solutions to this problem in traditional distributed platforms, a solution that explicitly takes advantage of the cloud paradigm has not yet been thoroughly investigated. The rubber band technique, which is inspired by the behavior of an elastic rubber band on a plate with several poles, has been exploited in this paper to design a solution to the problem. Our experimental results show that the proposed technique can effectively find an answer for the maximum flow problem in a graph. As the size of the graph in terms of number of nodes, number of edges and flow value increase, the proposed scheme outperforms in comparison to the selected benchmarks.