Abstract. Replication of content on geographically distributed servers can improve both performance and reliability of the Web service. Anycast is a one-toone-of-many delivery technique that allows a client to choose a content server of a set of replicated servers. Presenting numerous mirror content servers to a client implies the difficult problem of finding the best server in terms of network performance. We formulate an optimization problem of anycast flows assignment in a connection-oriented network. This is a 0/1, NP-complete problem, which is computationally very difficult due to the size of solution space and constraints. Therefore, we propose computationally effective heuristic algorithm. To our knowledge, this is the first proposal to solve the problem of anycast flow assignment in connection-oriented network. Results of simulations are shown to evaluate performance of proposed algorithm for various scenarios.