Abstract: The controllability analysis of underactuated flexible manipulator is a key problem to efficiently control the systems. In this paper, a 3DOF underactuated planar manipulator with flexible links is taken an example and its controllable analysis is performed by two steps. Firstly, the state controllability of the rigid systems is investigated at the different actuator placements regardless of the elastic deformations of links. Then, the structural vibration controllability of the flexible system is studied based on the discussion above. It is shown that the vibration controllability of underactuated flexible manipulators is both joint configuration-dependent and actuator placement-dependent. Moreover, the state controllability of underactuated rigid robot has important influence on the vibration controllability of the corresponding flexible system. Finally, the method is extended to underactuated planar flexible manipulators system with N degrees of freedom and one passive joint.