Abstract: A geometrically exact beam element suitable for dual nonlinear analysis is developed by the grounds of the BFGS update method of second kind. The high order Hermite function and Lagrange function are adopted to approximate the displacement field of an Euler-Bernoulli beam element and of a Timoshenko beam element. Studied were the nonlinear sectional behaviors without shear deformation, with shear deformation but not considering shear effect of stirrup and, with shear deformation and shear effect of stirrup. The first-order variation and the second-order variation of the sectional deformation of an Euler-Bernoulli beam element and of a Timoshenko beam element are deduced upon the geometrically exact beam theory, and the finite element procedure is presented upon the two-level consistent secant operator. The beam element developed upon UEL interface of software ABAQUS is employed to conduct the geometrical nonlinear analysis of elastic cantilever beams and, the material nonlinear and dual nonlinear analysis of reinforced concrete beam column components. The beam element proposed is suitable for large deformation and rotation analysis. The Timoshenko beam element considering the shear effect of stirrup has good applicability to analysis the nonlinear behaviors of reinforced concrete columns with different failure modes. The BFGS update method of second kind has a better numerical stability than that of BFGS update method of first kind.