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.