This paper describes the use of flexible multibody system approaches in the dynamic modeling of interconnected rigid-elastic robotic manipulators. Two approaches are used to establish the flexible robot dynamic model; the floating frame of reference formulation (FFR) and the absolute nodal coordinate formulation (ANCF). The ANCF is used with two different methods for formulating the elastic forces; basic continuum mechanics approach (ANCF-BC) and elastic line method (ANCF-EL). The simulation results show that the use of the nonlinear FFR and the ANCF-EL improves the performance of the beam element in the modeling of flexible robotic manipulators. In the case of simple large deformation shape, the simulation results obtained show a good agreement between the FFR and the ANCF solutions. In the case of thin and stiff beams, the coupled deformation modes that result from the use of the ANCF-BC can be a source of numerical problems. These problems can be avoided using the implicit Hilber-Hughes-Taylor (HHT) integration method. On the other hand, HHT integrator does not capture high frequency axial modes when the FFR is used; RADAU5 method is used instead. The experimental results of the direct dynamics model are effectively used in this study to validate the numerical solutions.