An equation of virtual work for geometrical non-linear vibration of a column with thin walled open cross-section, subjected to concentrated and distributed tangential follower loads, is derived by introducing the concept of initial stress, and stability problems of columns with channel section are investigated systematically and detailed by illustrating the space trajectories of eigenvalues. The five-term approximation of the extended Galerkin method is used, and the eigenfuctions of the flexural free vibration and the torsional one of a column are applied to the fundamental function which satisfies only the geometrical boundary conditions.