A concrete tower construction has a foundation and a plurality of prefabricated concrete tower elements, each having an outside, an inside, a material thickness provided there between, and top and bottom surfaces. The tower elements have hollow centers and are arranged one tower element on top of another, forming a column on top of the foundation. Plural tendons arranged in the hollow center apply tension force to the column. An upper force distribution element is arranged on top of the column, and a lower force distribution element is arranged in the foundation. Each tendon is connected to the upper force distribution element and the lower force distribution element by cooperating attachments. Methods of erecting the tower construction, tower elements and a foundation are described.