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We propose a novel algorithm for network reliability analysis, which is based on rational approximation. It uses rational functions to estimate the transformed reliability function and can be applied to estimate the k-terminal reliability measure and the reliability of networks with different protection algorithms. Experiments are used to demonstrate the effectiveness of the rational approximation algorithm. The algorithm uses far less simulation time than Monte-Carlo simulation and it can obtain the whole reliability function curve. It is easy to implement and can be easily added to network design analysis toolboxes.