Abstract: Based on the displacement variational principle and the strain-displacement relations of curved beams, the paper presents some fundamental nonlinear equations that describe the elastic behavior of thin-walled curved beams. The lateral buckling of thin-walled curved members with shear lag is analyzed. A transformed B₃ spline function is used to simulate the warping displacements of the thin-walled curved beams. The stability of the simple beams with I-shaped cross sections is studied. The method is shown to be versatile, accurate and efficient.