A floating vessel is equipped with perforated plates which exhibit both an added-mass effect and a damping effect. The addition of porosity to an added mass plate phase-shifts the added mass force so that it becomes at least partially a damping force which does not depend on large velocities to develop a large damping force. Preferred porosity is in the range of about 5% to about 15% of total plate area. A semi-submersible drilling rig may have damper plates fitted between its surface-piercing columns and/or extending from the sides of its pontoons. A truss spar offshore platform may have damper plates installed within its truss structure intermediate its hull and ballast tank. Drill ships and similar vessels may be equipped with damper plates extending from the sides of their hulls to reduce both heave and roll. In certain embodiments, the damper plates are retractable so as not to interfere with docking and to reduce drag while the vessel is underway.