At present Chernobyl Sarcophagus (CS) represents a structure, containing materials of core and fragments of building, formed as a result of accident at reactor number 4 of Chernobyl NPP and the subsequent work for localization of fissile and radioactive materials (with the purpose to prevent their harmful action on environment, population and staff). Nuclear danger of CS is connected with change of condition of fuel-containing masses. In turn the change of their condition can be forced by various initial events, external and internal. External events are earthquake, flood, aircraft accident, storm. To internal events it is possible to attribute incidents with flood, fire, explosion, collapsing, physico-chemical processes, causing appearance of dangerous fissile conglomerates. Real and hypothetical fissile substances, which need to be investigated on CS, represent homogeneous and heterogeneous systems with various compositions of fuel-containing materials (FCM). The solid radioactive wastes of CS include various modifications of FCM inside CS (fragments of core, graphite, dust, lava-like fuel-containing masses (LLFCM) and others). Besides listed LLFCM the fourth modification? water solutions of salts, is found out and investigated. In CS processes can take place, which result, at influence of the external factors, in formation of new types of fissile compositions. At present hot chemical reactions are known, and, as a result of these reactions, soluble uranium salts arise. These salts contain transuranium elements (TUE) and constitutional waters, are soluble in a water and can form water solutions of uranium and TUE in some interval of concentration. Liquid radioactive wastes (LRW) of CS include solutions, containing mainly nitrates and berates, various chemical elements and organic combinations. LRW of CS contain fissile materials (uranium, plutonium) in dissolved and colloidal phases, as well as contain FCM (suspensions, pulps, and others). In this work some problems of the nuclear criticality safety analysis of CS are considered.