T his paper is concerned with linearized elastic buckling analysis of columns. The Carrera unified formulation (CUF) is used to formulate variable kinematics beam theories. According to the CUF, Taylor-like polynomials of order N are used to interpolate the cross-sectional displacement field. By using the strong form of the principle of virtual displacements, governing equations and natural boundary conditions are formulated in terms of fundamental nuclei, whose formal expressions do not depend on the order of the theory N. The dynamic stiffness matrix is straightforwardly developed and the algorithm of Wittrick and Williams is used as solution technique to compute critical buckling loads for a number of solid and thin-walled metallic and composite beam-columns. The results computed using the proposed method are compared with those available in the literature. The accuracy and efficiency of the current approach as well as its capability to deal with bending-torsion and coupled buckling modes are demonstrated.