Abstract: The buckling of sway-prohibited columns takes the form of column’s bending, indicating the vanishing of the member stiffness against the bending deformation. In the light of the lateral buckling of frames where the axial forces are understood as negative lateral stiffness, the present paper proposed the concept of the equivalent negative flexural stiffness of axial forces in sway-prohibited columns. The positive physical flexural stiffness and the negative flexural stiffness of axial forces were studied, and formulae for both stiffnesses were proposed. The position of the maximum flexural deformation and the local bending second order factor were also investigated and formulae were presented. This study on the no-sway buckling of columns provided a simple and intuitive way of understanding no-sway buckling.