Abstract: Two spatial beam elements based on the geometrically exact beam theory are developed using high order Lagrange interpolation and Hermite interpolation. An element-level equilibrium iteration procedure is proposed for condensing out internal degrees of freedom, enhancing the applicability of the elements to general-purposed finite element software. A geometrically nonlinear analysis algorithm with both load control and cylindrical arc-length control is developed for spatial frame structures. The presented results of numerical examples show that the proposed approach is effective both to increase the computational efficiency and to achieve better numerical stability. Especially, the proposed element based on the Hermite cubic interpolation performs better in the numerical tests and is therefore well suited for the post-buckling analysis of frame structures.