This final thesis is dealing with explores theories related to the buckling of beams, with emphasis on inelastic buckling. In the theoretical part of the thesis, buckling is explained and a brief history of it is given, along with a short explanation of Euler's buckling expression, which is frequently used in calculations of elastic buckling since it matches experimental results quite well. Furthermore, the thesis discusses inelastic buckling theories, which do not match experimental results as well as Euler's formula does for elastic buckling. Among the inelastic buckling expressions, the most popular are Tetmajer's line and Johnson's parabola. However numerous expressions are discussed within this thesis. The numerical part of the thesis contains many examples followed by their solutions, and they illustrate all of the previously reviewed theories. Some examples were solved using many of these theories, with the goal of comparing the results. It is concluded that the „perfect“ theory or formula does not exist, but that it is necessary to be familiar with the specific situation, and whether a theory is appropriate for that situation (e.g. calculating the dimensions of columns in civil engineering) or if it has a more general application.