To improve calculation efficiency and accuracy of ultimate bearing capacity analysis for concrete filled steel tube arch, based on co-rotational procedure, a numerical model considering material and geometrical nonlinear analysis for concrete filled steel tube beam element is developed. Firstly, based on a linear relationship of strain in co-rotational coordinate system and deformation excluding displace of rigid body, by means of virtue work, a tangent stiffness matrix for material nonlinearity of perfectly-bonded concrete filled steel tube beam element is derived in co-rotational coordinate system without iteration. Then, by building total and incremental relationships derived from differential equations of nodal displacements and forces between global coordinate system and co-rotational coordinate system, respectively, tangent stiffness in global coordinate system concrete filled steel tube beam element is developed considering geometric and material nonlinearity, and unbalanced forces are calculated based on total relations. A comparison between the results in this paper and those from existed references demonstrates that the algorithm in this paper is highly efficient and accurate with many advantages such as non-cumulative calculation errors and reduction in computation.