The article presents static economic and mathematical models of behavior of the system "industrial enterprises –distribution network" in a competitive environment of the oligopoly type. A duopoly for industrial enterprises is modeled, the finding of an equilibrium solution of which is reduced to a pair of quadratic programming problems of the transport type. When solving problems related to optimizing the management of material flows in logistics or distribution networks, not only compensation and risk factors are taken into account, but also competition between manufacturers, suppliers, transport companies, forwarding companies, etc., which ensure the physical movement of material flows. An important feature of competition between several companies is that all competitors can influence the prices of products and raw materials. As a result, each firm's profits depend on the policies of other competing firms. But as for logistics, the known methods of analyzing the competitive environment require some modifications. For a special case, Solutions of the duopoly that are equilibrium according to Cournot and Stekelberg are found. The purpose of the article is to develop economic and mathematical models for the analysis of the duopoly "industrial enterprise-distribution networks" to determine equilibrium solutions and analyze the influence of the competitive environment on the optimal distribution of material flows moved from industrial enterprises to their final consumption sites. Models of movement of material flows in integrated logistics systems and optimal control of their movement in integrated logistics systems, built on the basis of static models of Multi-Index models of nonlinear programming of the transport type, are considered. Such models can be effectively used to describe, analyze, and optimize enterprise behavior in a competitive environment. Currently, dynamic optimization models based on the results of inventory management theory can be more effective for Strategic Planning. Models of this kind can be used to model oligopoly and oligopsony simultaneously. Solving this problem is a promising area for further research in the field of theoretical logistics and its applications.