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Anycast has been applied widely in service discovery and replicated service. Current researches on anycast routing mainly focus on the scenario that the anycast server is the final destination in a communication session. In this paper, we explore another scenario where anycast is applied for relay routing, and addresses the problem of selecting among the anycast relay routers. After analyzing the characteristics of anycast relay routing distinguished from general anycast routing, we present three selection algorithms for anycast relay routing, namely nearest to source, nearest to destination and random selection. Based on the results of probability analysis and simulation, we compare the performance of each algorithm, analyze how the placement and the number of relay routers impact the performance of selection algorithms, and further discuss how to apply these selection algorithms and how many relay routers should be deployed.