The goal of the work is to test the calculation method based on the application of the “rotational coefficient” in the rotation matrix of finite elements with the “seventh” (warping) degree of freedom and used in the design of thin-walled rod systems in the framework of the semi-sheer theory of V.I. Slivker. for the analysis of the stress-strain state of lightweight gauge steel structures (LGSS). The object of research is thin-walled plane rod systems (frames). The subject of research is the stress-strain state of thin-walled plane rod systems under the transverse bending load with an eccentricity on the example of a П-shaped frame. Method. The main research method in the paper is the finite element method. The software program ABAQUS is used to design and calculate 3-D solid finite element models of various joints and structures made of thin-walled profiles. Results. Тhe proposed method is correct for span sections remote from two finite warping-stiffness joints. The stress error for the most dangerous point of the most dangerous section was 4.3%. The stress values in the dangerous section, obtained by the proposed method, differ upwards from the "true" values, which gives a small margin of safety. At a distance from the dangerous section (in the middle of the crossbar) in both directions by a third of the span, the error gradually decreases to 2.9%; in the zone of joints the error was 9.2%, moreover, the stresses were lower than "true" ones. The distribution of the bimoment along the axis of the column and its values calculated using an inversed way and based on the solid finite element model are also much closer to the “true” ones than those, which were calculated without taking into account the “rotational coefficient”.