Vessel with mooring system, comprising a turret anchored to the seabed and a turret casing being part of the vessel, wherein the turret and turret casing are interconnected by a connecting element comprising a bearing arrangement and wherein the connecting element has a first end connected to the turret casing and an opposite second end connected to the turret. The connecting element is positioned in such a manner that it experiences tensile forces. When the turret downwardly loads the turret casing the first end of the connecting element is positioned at a higher level then the second end thereof. When the turret upwardly loads the turret casing the first end of the connecting element is positioned at a lower level then the second end thereof.