The dynamic analysis of link structure, including both flexible and rigid bodies is developed in this study. The model of flexible body is based on FEM theory, and geometric nonlinearity effect is taken into account. The theory proposed in this study is improved about the problem of numerical integration error in the former theory. Moreover, in the flexible-rigid link structure, dependent variables are eliminated using the topological information. In general, Lagrange multiplier technique is used for the analysis of this system. In this method, the equation of the system is the form of DAE and it is not be able to be solved efficiently. On the other hand, the equation of the total system obtained in this study is the form of ODE and it is able to be solved efficiently