Starting from the principle of virtual displacement for 3-dimentional continuum subjected to the initial stress, the finite element formulation for the buckling and free vibration analysis of the unsymmetric space beam is presented based upon the displacement field which includes the effect of restrained warping torsion but neglects the shear deformation. Hermitian polynomials are used as the shape function for the lateral displacement and twisting angle. By deriving the elastic stiffness, the geometric stiffness matrix and the mass matrix, the matrix equation of motion for the two space beam element (6, 7 degree of freedom) is obtained. Example problems, for which exact solutions are konwn, illustrate the accuracy and convergence characteristics of the derived formulations.