Abstract: The invention provides a tower construction e.g. for a wind mill and a method of laying a foundation of a tower construction. The tower construction (1) comprises a concrete element (2), and a base flange (3) from which a tower wall (4) extends upwardly. The base flange is supported by an intermediate support structure (5) positioned on the concrete element (2). The support structure (5) is more rigid than the concrete element (2) and comprises a resilient pressure distributing element (6) which is soft relative to the concrete element (2). Furthermore, the invention provides a support structure for a tower construction.