In this paper we consider the fair flow problem in multiple source multiple sink network, as applied to telecommunication networks. We present an iterative algorithm for computing fair routing in networks where the available resources are shared among competing flows according to a max-min fair sharing criterion. Our main objective is computing optimal routing paths, with regard to max-min fairness, in stable and known traffic conditions. It is a linear programming based approach which permits a lexicographical maximization of the vector of fair-share attributed to the connections competing for network resources. An optimality proof and some computational results are also presented.