A Content Distribution Network (CDN) can be defined as an overlay system that replicates copies of contents at multiple points of a network, close to the final users, with the objective of improving data access. CDN technology is widely used for the distribution of large-sized contents, like in video streaming. In this paper we address the problem of finding the best server for each customer request in CDNs, in order to minimize the overall cost. We consider the problem as a transportation problem and a distributed algorithm is proposed to solve it. The algorithm is composed of two independent phases: a distributed heuristic finds an initial solution that may be later improved by a distributed transportation simplex algorithm. It is compared with the sequential version of the transportation simplex and with an auction-based distributed algorithm. Computational experiments carried out on a set of instances adapted from the literature revealed that our distributed approach has a performance similar to its sequential counterpart, in spite of not requiring global information about the contents requests. Moreover, the results also showed that the new method outperforms the based-auction distributed algorithm.