The principles of formation of mathematical models for the choice of rational modes of operation of complex gas transmission systems with multi-shop compressor stations equipped with different types of gas pumping units are given. It is proposed to optimize the modes on the basis of the use of energy-economic characteristics of the gas transmission system, which are built on the basis of the parameters of the gas transmission system taking into account the technical condition of its elements and economic performance for a certain period. This approach ensures compliance with the principle of operation of the gas transmission system in the field of permissible modes and maximum energy consumption on the one hand and minimizing the cost of gas transportation on the other. If it is possible to use the actual data on the actual technical condition of the equipment and gas pipelines of the system, this method allows to evaluate and take into account in the further procedure the parameters of gas supply reliability. An important requirement for the optimization procedure is the stability of energy efficiency characteristics, which means that in any practical changes of non-basic regime parameters, the energy efficiency characteristic should not be shifted beyond the allowable error. The problem of optimal load distribution in a complex gas transmission system is considered based on their minimum total energy costs at a given volume of gas supply and other planning and technological constraints. The task of optimizing a multiparameter object is to find the extremum of the goal function by selecting a vector of control effects that would satisfy the constraint. The distribution of loads at the highest hierarchy for the system of main gas pipelines is obtained by finding the minimum total cost of gas compression for each pipeline. The method of construction of such characteristics and the procedure of establishing their stability are shown, which allows the formalization of the construction of the criterion dependence of the regime parameters on energy economic factors. The stated basic decisions allow to formalize the function of the purpose for a choice of a rational mode of operation of gas transmission system in the conditions of its incomplete loading