Analysis of scientific publications on the assessment of resistance of structures to progressive collapse, as well as existing and projects of design codes of different countries, in particular the project of Design Code "Protection of buildings and structures against progressive collapse. The design requirements. General conclusions", shows, that the main evaluating criteria are strength parameters. At the same time, structures, which are made of high– strength materials and have small sizes of cross-sections, as well as structures operating in aggressive conditions, when the cross-section decrease or the computational length suddenly increase, should be checked to the loss of stability of the bearing elements. The purpose of this study is to obtain the evaluating criteria of the survivability and residual life of reinforced concrete (RC) structural systems at sudden loss of stability of the element, caused by the evolutionary accumulation of a critical level of corrosion damage. The article presents analytical dependences to determine the critical value of the cross-section stiffness of the corrosively damaged element and the critical time, after which the structural system lose stability in conditions of simultaneous action of forces and aggressive environmental influences. Proposals are given to assign the survivability parameters of reinforced concrete structural systems, operating under exceeding limit states, that caused by the sudden loss of stability of the carrier element at the accumulation of critical value of corrosion damages.