The calculating stability of an engineering structure against progressive collapse is considered in this article. The calculations results are analyzed. A dangerous emergency scenario was developed and measures were developed to prevent the progressive building collapse in the structures local destruction in accordance with the regulatory documents requirements for such an object. The most dangerous design schemes are considered to assess the structure stability against progressive collapse. A scenario for calculating stability against progressive collapse in the case of local failure has been selected, and a consistent action algorithm has been obtained that makes it possible to perform a calculation for resistance to progressive collapse., The kinematic method of the limit equilibrium theory for structures with elastic-plastic materials properties is used to calculate the resistance to progressive collapse. It corresponds to the turning the system into a plastic kinematic chain, the links movement is carried out due to the plastic flow of the system's links. Two types of undamaged structures were identified to assess the building resistance to progressive collapse: neighbouring beams and columns, in which local destruction impact does not cause a qualitative change in the stress state, but leads to an increase in stresses and forces (neighboring beams, columns); pavement slabs resting on a beam and welded through embedded parts to a beam that has lost its original support, and located above a local fracture, the stress state changes. The conclusion is made about the requirements that should be met in order to conclude the calculation justification so it can be said that resistance to progressive collapse is ensured. It has been established that the calculations performed confirm the object stability - the drainage chamber to progressive collapse in the local destruction as an emergency situations result.