The problems of instability of steel frame structures have been of interest to many investigations for a long time. The fast development of computer technology has created the possibility of a complete solution to such a problem. This paper briefly presents one numerical procedure for the global stability analysis that is based on the FEM. The stiffness matrices are derived using the trigonometric shape functions. Also, when the buckling of the structure occurs in the inelastic domain, the tangent modulus theory is applied. Obtained results show justification for applying such a procedure for the stability calculation of the frame structures.