Abstract: Based on the absolute nodal coordinate (ANC) framework, the dynamics modeling and solutionstrategy for the multibody system with fractional derivative damper is investigated. The flexibleparts are discretized by the ANC-based locking-free shear deformable beam element. The systemequations of motion with constant mass matrix are also obtained and solved by the numericaldissipation controllable generalized-a method. The effects of the algorithm parameter and thefractional index on the dynamics responses are also studied by solving the numerical examples.The presented procedures can also be used to solve many other practical engineering problems.