A technique for selecting a network node from a plurality of nodes employing anycast addressing based on a priority. The plurality of nodes is configured with an anycast address. At each node, the anycast address is associated with a unique priority value that represents a priority associated with the node. Traffic destined for the anycast address is forwarded to the node whose priority value indicates the highest priority. If the node becomes unavailable, traffic destined for the anycast address is forwarded to a node whose priority value indicates the next highest priority, and so on.