A supporting system for a floating unit in shallow water exerts controlled stresses on the floating unit hull and includes supporting structure for the hull. An extendable supporting device operatively connects to the supporting structure and is suitable to support a predetermined weight of the floating unit and load when entirely supported by the extendable supporting device and when the extendable supporting device rests on a bed of a water body. An actuator device connects to the supporting structure and operatively connects to the extendable supporting device for extension or contraction. A control device operatively connects to the actuator device to control the extraction or contraction movement of the extendable supporting device. The system includes at least one hull stress monitoring device operatively connected to the control device. A device to monitor the stress, or load, on the extendable supporting device operatively connects to the control device.