Abstract: A stabilization device is for a wellhead wherein an upper portion of a wellhead casing extends up above a seabed, the upper wellhead casing portion being sideways supported in a suction substructure. A blowout preventer extending up from the upper portion of the wellhead casing is provided with multiple supporting elements abutting supportingly an edge portion of an end cover on the suction substructure. A method is for stabilizing a wellhead wherein an upper portion of a wellhead casing extends up above a seabed and is sideways supported in a suction substructure surrounding the wellhead casing portion and extends downward in an uncompacted material.