This article presents a novel, approximate method that makes it possible to analyse multi-service switching networks. The method belongs to the group of the so-called effective availability methods and is characterized by very high accuracy for single-service and multi-service switching networks alike. The operation of the proposed method is presented with an example of a number of three-stage switching networks with different ways of the execution of inter-stage connections. A comparison of analytical and simulation results confirms high accuracy of the proposed method that is independent of the structure of a switching network.