Abstract: Variable structures are widely used in civil and aeronautic engineering, such as the deployable shelter and foldable antenna, etc. The mutibody dynamics of the finite element method with natural coordinates is used in this analysis. Based on the minimum strain energy method with the rigid body hypothesis and the Lagrangian multiplier method, the fundamental equations construction of multibody kinematics is given. And based on Hamiltonian theory, the fundamental equations construction of multibody dynamics is illustrated. The convergence principle of numerical simulations is also investigated. An analysis program is written with MATLAB software. By simulating a planar double pendulum, the results indicate that the numerical damper should be considered to ensure numerical stability and precision. Finally, the motion analysis of a four-bar linkage is carried out to verify that the proposed method can be used to simulate the deployment of variable member structures.