An artificial island located on the high sea is formed of a support structure and a platform mounted on the upper end of the support structure. During erection, the support structure, not completed for its full height, is moved into position and founded on the ocean floor. The platform is floated into position and mounted on the upper end of the support structure. The height of the support structure is then extended until the final height is reached. During the completion of the upper end of the support structure, the platform is lifted so that it remains on top of the support structure. A housing is provided around the upper end of the support structure so that it can be sealed from the environment for completing the construction of the upper end of the support structure.