Introduction. The results of the studies analysis on the protection of multi-storey buildings from progressive collapse are presented, which indicates insufficient attention to structural systems made of precast reinforced concrete, as a result of which design standards orient the designer to the use of not always effective monolithic structures. In particular, the problem of protection against progressive collapse with the exclusion of prefabricated crossbars of floors and coatings has not been practically studied. The purpose of the study is to develop a method for calculating a continuous system of hollow plates made by the method of formless molding.Materials and methods. When designing the protection of multi-storey buildings from prefabricated elements, a static calculation is usually carried out with the exception of vertical structures (walls, columns) and the reinforcement of floor crossbars and coatings by ensuring their continuity. There are constructive methods of reinforcing prefabricated floors by creating continuous plates of adjacent spans with the help of connecting elements made of plastic reinforcing steel, but the calculation of such systems has not been developed. A method for calculating a system of two plates according to a rigid thread scheme is proposed.Conclusions. Currently, theoretical methods have been developed to solve various problems of protecting buildings and structures from progressive collapse. However, there are many design requirements for the protection of multistorey buildings from progressive collapse, which have not yet received experimental and theoretical confirmation for the effective solution of practical problems. It seems that in this article one of these problems is partially solved.