This paper considers the phenomenon of the instability of steel plane frame structures in the elastic–plastic domain. The numerical analysis uses finite element method, where the corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. The tangent modulus concept is applied when buckling occurs in the plastic range. Thus, the stiffness matrices for nonlinear material behavior are also derived. The procedure for determining effective length factors of compressed columns, which implies a global stability analysis of entire frames, is established too. It means that the proposed approach is based on the assumption that the collapse of the structure occurs when the most loaded columns reach their stability limit. So, the presented procedure enables the calculation of the real critical load of plane frame structures in the elastic–plastic domain and determines the corresponding effective length factors.