For free motions, vibration suppression of flexible manipulators has been one of the hottest research topics. However, for constrained motions, a little effort has been devoted for vibration suppression control. Using the dependency of elastic deflections of links on contact force under static conditions, vibrations for constrained planar two-link flexible manipulators have been suppressed successfully by controlling the contact force. However, for constrained spatial multi-link flexible manipulators, the vibrations cannot be suppressed by only controlling the contact force. So, the aim of this paper is to clarify the vibration mechanism of a constrained, multi-DOF, flexible manipulator and to devise the suppression method. We apply a concise hybrid position/force control scheme to control a flexible manipulator modeled by lumped-parameter modeling method. Finally, a comparison between simulation and experimental results is presented to show the performance of our method.