In modern society in Russia and abroad there have been observed a wide application of a metalware in industrial and civil engineering. Special place in the building industry is belonged to light steel thin-walled constructions, which have a lot of technological advantages. In the monolithic and frame building, which amount constantly grows it is possible to use so-called thermopanels as effective and economic protecting designs.

The purpose of this work is to create a numerical method of thin-walled bar systems design by using semi-sheared and unsheared theories. In the article the first development cycle of a numerical method creating is considered – creating of the matrixes of the inflexibility of thin-walled finite elements of various types using the semisheared theory (by V.I. Slivker) – depending on a way of approximation of deformations functions (torsion and warping):

1) linear approximation of torsional functions with a 2-central finite element having 4 transitions;  2) square-law approximation of torsional functions and linear approximation of warping function with a 3-central finite element having 5 transitions;  3) square-law approximation of functions of torsional and warping functions with a 3-central finite element having 6 transitions.

Thus deformation functions (torsional angle and warping) are approximated as mutually independent functions.

Also creating of a matrix of the inflexibility of a thin-walled finite element on unsheared theory of design (by V.Z. Vlasov) with cubic approximation of torsional functions is considered.