The advancement of technology of the building materials through the development of new methods of production and processing, makes it possible to create members with almost any geometry and shape, as well as thickness, which, in combination with the introduction of finite element analysis software, led in the use of increasingly thin members and constructions, which are subsequently sensitive to different forms of buckling. The set of methods for calculating the critical buckling loads for the different forms of manifestation of geometry nonlinearity are not analyzed in the design methods of Eurocode 3, but are described in detail in the provisions of the new CEN/TR 1993-1-103. The object of this thesis is the creation of appropriate applications of the individual chapters of the standard, in order to evaluate their reliability, but also the coexistence with the corresponding design methods of ΕΝ1993-1-103. The selection of the various examples is also intended to highlight cases of particular interest and several uncertainties. More specifically, it is to be studied, the flexural buckling of a cantilever of non-uniform section under compression, the buckling of the upper chord of steel truss bridge, a mono-symmetrical cross-section of single symmetry under compression which undergoes torsional-flexural buckling, a second mono-symmetrical cross-section under bending that manifest lateral buckling, but also the stiffness value required, for an elastic constraint, to be considered fixed. In addition, both the theoretical background and the application method of the single local and global imperfection in the shape of elastic critical buckling model (UGLI) have been analyzed, which seems to be the most effective way to universally treat the imperfections in most of the cases of structural steel members. Lastly, it is worth noting that a key ally during the completion of this diploma thesis was the set of non-linear analysis, which provided necessary information both for the behavior and the strength of the various members and structures. Consequently, at the end of each chapter, one can tell whether it is necessary to apply non-linear to the individual examples.