A veil section of a hyperbolic natural draft cooling tower is constructed on a lintel beam in the form of a closed planar curve provided with anchors spaced about the perimeter of the lintel beam for facilitating connection to the lintel beam of upstanding peripherally spaced column sections between which preformed panels are attached to fill the spaces between the spaced columns. Once the panels are affixed to the columns, the latter, as well as the adjacent portions of the adjoining panels, are encased in a cementitious material such as concrete. Additional sections of columns and panels are erected above the initial veil section by the same process as the latter in order to complete the veil. Vertically adjacent veil sections are attached to one another by connection of the columns in end-to-end relationship.