Since the beginning of the XXI century the use of light steel thin-walled structures made of roll-formed profiles in industrial and civil construction is growing rapidly. The use of such structures has given impetus to the development of the whole industry including the design, manufacture and installation of structures using thin-walled cold-formed sections of galvanized steel. The purpose of the review, given the importance of the analysis of thin-walled steel structure bearing capacity and stability, is a compilation of the major theoretical calculations exploring the stress-deformation condition of the structures, together with experimental evidence and examples of mathematical modeling. The article is devoted to analytical review of existing publications by Russian and foreign authors on the topic of analysis of steel thin-walled rods. This article compiles the most significant work devoted to the theoretical foundations of calculation of thin-walled beams in the formulation of static, dynamic problems and buckling. Special attention is paid to the loss of local sustainability and reduction in cross-section in the calculation of the elements. Papers describing the application of the developed theories of stress-strain state in the structural calculations using finite element systems were reviewed