Monograph . - M. : Editorial URSS, 2014. — 800 s. The monograph contains a detailed description of practically significant technologies of high-precision computer modeling of a wide range of product flow modes through systems of extended pipelines or open-bed channels. including having a complex topology or functioning under critical conditions. Depending on the problem to be solved, gas mixtures, multicomponent liquids and gas-liquid media can act as transported products. The proposed technologies can easily be extended to the numerical analysis of flows of multiphase media with solid inclusions, provided they are finalized according to the methodology presented in the book .. Much attention in the monograph is paid to a detailed description of the sequence of reasoning , which led to the construction of a mathematical model or the development of algorithms for its numerical analysis including scientifically based research of promising and dead-end branches of their further development. In the book, a special place is given to the mathematical aspects of monitoring the functioning of the main and gas distribution systems operated in the gas industry. At the same time, there are ways to predict the optimization of costs for the full range of modes of natural gas transportation, algorithms for preventing emergency situations .. The monograph offers effective methods of numerical recovery of non-stationary transport flows of gas mixtures through branched looped pipelines and an approach to the automated adjustment of the parameters of the design model to the characteristics of real pipeline networks in the conditions of shortage of measuring information. The presentation of the material in the book was carried out on the basis of a single concept of numerical modeling of backbone systems, which greatly simplifies its development and practical application. The proposed technologies of high-precision computer modeling of currents in mainline systems have found practical application in the industries of the fuel and energy complex of mechanical engineering and medicine , as well as in the development of advanced samples of high-precision small arms. The book can be useful to researchers, graduate students and teachers engaged in mathematical modeling, the creation of applied software and mathematical support and carrying out computational and analytical work associated with the research of pipeline and channel systems .. The material of the monograph is available to senior students of technical universities.