Introduction. Lean supply chain management is one of the areas of management in supply chain management, it is based on the philosophy of continuous improvement and elimination of waste. This direction has a large number of branches and modifications. The purpose of this work is to study such tools and methods of supply chain management as Value Stream Mapping System, Kanban System, Production Total Quality Management. Materials and methods. The article presents the advantages, problems and limitations of lean supply chain management methods. As advantages, the improvement of the quality of manufactured products, the creation of a socially responsible business model, the reduction of waste and the conservation of natural resources, the increase in customer satisfaction, the reduction of lead times and the increase in the company's competitiveness in the market are named. The main limitations in implementing lean supply chain management principles can be the high initial investment required for implementation, resistance to change by suppliers and employees, the difficulty of measuring results, especially in terms of quantifying its impact on customer satisfaction and profitability. The article provides examples of overcoming emerging limitations. These examples highlight the importance of careful planning, implementing and monitoring lean initiatives to ensure their success in the supply chain. Results. In the course of the study, a review of approaches to the implementation of lean supply chain management was carried out, the positive and negative aspects of each approach were considered, taking into account modern modifications and the experience of their application. In conclusion, a review of the literature is made and the main directions for further research are identified.