The design and construction of the Shelter Object was carried out in a record short time in extreme radiation hazardous conditions, which did not allow the object to be constructed in accordance with the rules and regulations for the design of not only nuclear installations or facilities for radioactive waste management, but also as ordinary industrial buildings. According to the results of on-site inspections and calculated assessments of the technical state of the Shelter Object building structures, which were carried out throughout its existence, structures with an unacceptably high probability of collapse (socalled unstable structures) were identified. Urgent stabilization measures implemented in 2004–2008 provide an acceptable safety level of the Shelter Object in terms of the short-term operation period of its stabilized building structures. In the future, the problem of unstable structures should be resolved by dismantling them inside the New Safe Confinement (NSC). The list of unstable building structures of the Shelter Object, which are subject to dismantling, was determined during the research implementation within the framework of the Shelter Implementation Plan [2, 3]. A main cranes system (MCS) is provided in the NSC for dismantling the Shelter Object unstable structures. The main characteristics of the MCS are given. It is shown that the dismantling of most unstable structures can be carried out using MCS in the reverse sequence of their installation during the Shelter Object construction. However, the dismantling of some structures requires additional equipment and special preliminary work. These include the Mammoth Beam, the weight of which exceeds the carrying capacity of the MCS, and the units of shields-sealers, which are located outside the MCS operating area. Technological solutions are proposed for the Mammoth Beam dismantling by installing a temporary support in the middle part of the beam span in order to cut it into two parts that can be alternately dismantled by the MCS, as well as technological solution for dismantling the shields-sealers units using a special traverse.