In this paper, the distributed parameter transfer function method is applied to analyzing the vibration and stability of composite combined beams under axial compression. The Hamiltonian formalism of a modified mixed variational principle about the symptic variables is established using Legrendre transformation with spatial variable as independent variable instead of time. The state-space equations in Laplace transform domain is derived from using Hamilton's principle and Laplace transform. The unified and closed form transfer function solutions are obtained for vibration frequencies and buckling loads under arbitrary boundary restrictions. The influences of the first and high order shear deformation, torsion deformtion, rotary inertia, length-to-thickness ratio and material anisotropy on natural frequencies and buckling loads are investigated. Numerical examples are provided to demonstrate the efficiency and suitability of the methodology.