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The aim of the study is to develop a European gas transmission system probabilistic model to analyse in a single computer model, the reliability and capacity constraints of a gas transmission network. We describe our approach to modelling the reliability and capacity constraints of networks elements, for example gas storages and compressor stations by a multi-state system. The paper presents our experience with the computer implementation of a gas transmission network probabilistic prototype model based on generalization of the maximum flow problem for a stochastic-flow network in which elements can randomly fail with known failure probabilities.The paper includes a test-case benchmark study, which is based on a real gas transmission network. Monte-Carlo simulations are used for estimating the probability that less than the demanded volume of the commodity (for example, gas) is available in the selected network nodes. Simulated results are presented and analysed in depth by statistical methods.