Abstract: A chimney construction arrangement in which the load-bearing external trunk is built in sliding or climbing shuttering and supports platforms with support arms for accommodating the flue gas pipe or the flue gas pipes. Support elements are formed on the inner wall of the external trunk at the planned levels of the platforms. The platforms are built completely within the external trunk at ground level and raised to respective levels with lifting equipment. The platforms are connected with the support elements. The support elements may be individual brackets. A plurality of platforms may be raised as a group and individually attached to the support elements.