Abstract: The dynamic analysis of multibody systems is carried out in this paper based on Gauss constraint principle, for a family of multibody open loop chain structures.  Gauss constraint method is used to derive the dynamic equation of multibody chain structures, in a symbolic derivation process, and the analytic expressions of the dynamic equation are obtained in closed form. By taking the rigid and flexible structures as examples, the time used for symbolic derivation of dynamic equations is analyzed for different analysis methods and degrees of freedom. It is shown that Gauss constraint method is more suitable for symbolic derivation of dynamic equations of multibody structures compared with Lagrange's method. Furthermore, the calculation advantage of Gauss constraint method increases with the increase of degrees of freedom.