Variational formulation of stability problems for thin-walled beams is presented. Geometrical stiffness matrix is derived from the stability functional. Shear deformation is taken into account by using V.I.Slivker’s semi-shear theory of thin-walled bars. Quadratic Hermite polynomials were considered as approximation for all the internal forces and displacements functions. The exact analytical solutions to some particular eigenfrequency and stability problems for thin-walled beam are obtained. The effect of «spurious» frequencies in thin-walled beam spectrum is discussed. Comparison of the numerical results from the finite element methods is presented. Approximation by quadratic functions turns out to be faster in cases where the buckling has a flexural-torsional form.