Abstract: For rigid-flexible coupling dynamic problems with large rotation and large deformation, the modeling method based on the local frame formulation (LFF) of SE(3) group can avoid geometrically nonlinear problem caused by the rigid-body motion. In discretized flexible multibody systems, the generalized mass matrix and the tangent stiffness matrix are invariant under the arbitrary rigid-body motion, which can improve computational efficiency significantly. In the finite element method, locking is the main reason for low convergence rate of elements, such as shear and Poisson locking in beam elements. Mixed methods are effective strategies to alleviate locking in beam and plate/shell elements. In these methods, not only the displacement field but also the stress field and the strain field are discretized, which can increase the accuracy of stress and strain. Based on the local frame formulation, the paper studies locking alleviation techniques of several beam elements, including geometrically exact beam formulation (GEBF) and absolute nodal coordinate formulation (ANCF) beam elements. The Hu-Washizu variational principle is used to alleviate shear locking in the geometrically exact beam, while the strain split method is used to eliminate Poisson locking in the fully parameterized ANCF beam. Numerical examples show that the proposed beam elements based on the local frame formulation can eliminate geometrically nonlinearity caused by the rigid-body motion and can minimize the updating times of mass matrices and tangent stiffness matrices when modeling flexible multibody systems with high rotational speed or large deformation. After locking alleviation, the convergence rate of the above beam elements improves significantly.