This paper focuses on grasping and manipulation of an object by two one-link flexible arms. By taking rolling constraints between the arm tip and the grasped object, the arms have the potential to grasp and manipulate an object at the same time. To realize grasping and manipulation by two flexible arms, a boundary controller is derived from a Lyapunov functional related to the total energy of a dynamic model described by a hybrid partial differential equation-ordinary differential equation (PDE-ODE) model. The derived controller consists of the bending moment at the root of the arm, the rotational angle, and the angular velocity of the motor. In particular, the controller does not need the feedback of the information of the grasped object, and thus, it is easy to implement the controller. Further, it is shown that the derived controller realizes stable grasping and orientation control of the object as well as vibration control of the arms. Finally, experiments and numerical simulations are conducted to investigate the validity of the derived boundary controller.