A damping (or heave) plate comprises a generally flat plate attached, beneath the surface of a sea, and in horizontal orientation, to a structural member subject to being vertically moved in response to passing surface waves. The plate tends to resist vertical movements and has the effect of adding mass to the structure. A vertically extending structure is added to both major surfaces of the heave plate for increasing the volume of water moved by the plate. For minimizing drag forces generally created by use of the damping plate, the vertically extending structure is shaped to include curved hydrodynamic surfaces for minimizing turbulence in the surrounding water.