The monograph contains a detailed description of the new edition of the concept and new methods of high-precision numerical modeling of main pipeline systems. The proposed concept and methods are the basic elements of the theoretical foundation of modern computer analytical tools for effectively solving a wide range of technical and technological design problems. construction and operation of pipeline transport facilities during their life cycles. They confirmed the reliability and efficiency of their practical application in solving production problems characteristic of the fuel and energy complex. The material presented in the monograph logically develops and complements the theoretical developments presented by the same authors in the book "Mathematical modeling of pipeline networks and channel systems: methods, models and algorithms" .. This book was published by MAKS Press in 2007. It should be noted that working with this monograph does not require readers to first get acquainted with