This paper presents a stress analysis of elements made of a steel cold-formed sigma cross-section, uniformly loaded in a plane parallel to the web and not passing through the shear centre. Such an application of a load very often occurs in engineering practice and corresponds to the application of a load to the upper flange of the cross-section. It usually result in an additional torsional moment. In this paper, special attention is paid to normal stresses from the bi-moment, and shear stresses from restrained and free torsion. The contribution of these stresses to the section utilization was evaluated on the example of a sigma cross-section with different thicknesses of the wall. Furthermore, the paper also included the stresses analysis concerning different load locations at the upper flange. All numerical calculations were made using analytical approach based on Vlasov beam theory.