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This paper describes an approximate method for evaluating the blocking probability of a switching network. The model used is C. Y. Lee's probability linear graph. By changing the structure of the graph between a pair of adjacent stages in two ways, it is possible to obtain upper and lower bounds for the blocking probability. The calculation of the bounds is performed on graphs which have a simpler structure as a result of the changes made. A suitable form is then chosen for the approximate blocking probability within the bounds. Typical multistage networks are treated in this fashion, and the approximate results are compared with the accurate blocking probabilities. The method is simple and inexpensive and produces reasonably accurate results.