Dynamic　control　of　the　underactuated　flexible　robot　in　operational　space　is　implemented　with　robot　end　variables　directly　used　as　the　control　objectives.　Firstly,　the　dynamic　equations　in　operational　space　are　derived　using　the　assumed　modes　method.　Kinematics　and　dynamics　of　the　system　are　analyzed.　Secondly,　position　control　method　is　proposed　based　on　the　dynamic　model　in　operational　space.　Then,　according　to　the　characteristics　of　the　nonholonomical　redundancies,　the　nonholonomical　self-motion　optimal　control　strategy　is　presented.　Finally,　simulation　of　a　3DOF　underactuated　flexible　manipulator　is　completed　and　the　results　verify　the　validity　of　the　presented　control　methods　in　the　operational　space.　The　conclusion　can　be　drawn　that　the　elastic　vibration　is　suppressed　to　a　certain　extent　via　the　nonholonomical　self-motion　optimal　control　strategy.