Stiffness matrices for geometric nonlinear analysis of thin-walled tapered members, applicable to large displacement problems, are derived and incorporated into a finite element program. Based on the assumptions by Vlasov on the thin-walled beams, the stiffness coefficients are obtained form the total potential energy expression by using the artificial intelligent symbolic package, MACSYMA. For illustrative purpose, elastic and inelastic buckling analyses are carried out on various single-member structures and on a planar frame. The results show that predictions from the present finite element program are more accurate and consistent than those from the existing ones. It is also found that the use of the conventional stiffness matrices from the standard energy theorem may lead to large errors even in a simple structure. The flexural strengths of tapered members of various taper ratios and moment gradients are computed and compared with the design code predictions.