Abstract: A gravity anchor for a tethered buoyant platform comprises a container ballasted with a heavier than water ballast such as drilling mud. The anchor is installed by (a) floating the container in a buoyant condition with its interior volume containing air to the offshore installation site, (b) admitting water to, and expelling air from, the interior volume to reduce the buoyancy of the container so that the container is either of reduced positive buoyancy or negatively buoyant, (c) either pulling the container down to the sea bed against its reduced positive buoyancy or lowering the container to the sea bed employing its negative buoyancy, (d) admitting a heavier than water ballast to the container and expelling the water therefrom to further reduce the buoyancy of the container to increase the stability thereof on the sea bed.