This paper discusses a grasping, orientation, and position control of an object by two flexible arms modeled by the Timoshenko beam. By utilizing our previously proposed controller for the cooperative control, we realize to control the grasping force, orientation, and position of an object as well as to suppress the vibration of the flexible arms. In particular, the closed-loop system is formulated in a Hilbert space, and the exponential stability of the closed-loop system is shown by the frequency domain method. The lightweight flexible arm has intrinsic elastic compliance, and thus the grasping by the flexible arms is safer than that by the rigid arms. In addition, the exponential stability of the closed-loop system contributes to the performance improvement of the grasping and manipulation of an object. Finally, experiments are conducted to confirm the validity of the stability analysis.