In this paper, the advantages of the general method for verification of the lateral torsional buckling are demonstrated through the calculation of a real steel frame with variable cross-section in Germany. According to the Eurocode 3, the minimum load amplifier of the design loads and the minimum amplifier for the in plane design loads to reach the elastic critical load with regards to lateral or lateral torsional buckling are determined with the linear buckling analysis and the geometrically and materially nonlinear analysis using finite element method. The results show that shell models can create arbitrarily complex cross-sections and obtain more accurate results comparing to beam elements. Finally, the practical implementation of the reinforcement of steel frame is shown.