One key technology for the offshore development of the increasing water depth will be remotely operated installation and construction of flexible structure in the deep water or on the seabed. The flexibility comes from scale-up or weight reduction of the structure. Conventional operation from the sea surface is affected by the weather conditions, and, therefore, not so efficient. This paper presents basic research on active control of elastic response and rigid body motion of an underwater elastic structure toward the remotely operated installation technique. The numerical model of the dynamics of the structural model is formulated, and based on the numerical model the control is formulated. The formulated control is tested by computer simulations and model experiments. The structural model is propelled by thrusters and taken from initial position to another position, while the elastic responses are controlled by variable buoyancy-type actuators.