The article discusses the modeling of the use of digital twin technologies (a digital twin) for the task of organizing long-term storage of various types of documents. A digital twin in this respect differs from a digital copy, which has no connection with the real original object. A review of the problem was carried out. We argue that, despite the active use of digital twin technology in various areas, its applications in the area of long-term storage of documents remain limited. At the same time, the task of increasing the durability of documents during long-term storage remains important and largely unresolved. The complexity of solving the problem of long-term storage of documents is considered, and a formal statement of the problem of long-term storage using digital twin technologies is carried out. Destructive factors that affect long-term storage documents and significantly reduce their durability have been identified. A system of indicators has been developed to assess the durability (preservation) of documents. The modeling of the use of digital twin technology in the organization of long-term preservation within the framework of Industry 4.0 was carried out. In the course of modeling, the goals and the strategies of long-term storage were established. Primary mathematical models for controlling destructive factors as well as technological solutions for digital twin long-term storage are proposed. It is assumed that the key part of this technology is the Industrial Internet of Things. The effectiveness of the use of digital twin technologies for solving the problem was assessed. The spheres of application and further ways of research are determined.