This paper presents three recursive algorithms for computing end-to-end blocking probabilities in a network with alternate routing, based on link blocking probabilities. The only assumption made is the statistical independence of link blocking probabilities. The first algorithm applies to arbitrary routing plans. The second algorithm applies to single-loss-route routing plans which include predictive routing plans used in advanced private networks. The second algorithm is also applicable to solving the terminal-pair reliability problem. The third algorithm applies to tandem-node-matrix-generated routing plans which include hierarchical routing plans similar to those used in North American public toll network, AT&T's CCSA, EPSCS, and ETN networks. These three algorithms are progressively more efficient.