Network resources are imperfect and vulnerable to failure from a wide variety of sources. Survivability is a well-researched field that focuses on strategies to prevent or reduce the harm inflicted when network elements fail. Solutions tend to either provision resources, such as backup paths, proactively so that traffic can be switched to the alternative route after a failure, or quickly find new resources to provision after failure event occurs. Current survivability solutions guarantee protection against these failures, but there is no mathematical model to calculate the network blocking probability for survivability solutions of anycast communication. In this paper, we developed new analytical models to calculate network-wide blocking performance for anycast survivability approaches. Performance results show that our models are accurate and are verified by extensive simulation results.