<p>An industrial cooling tower comprising a support structure resting on a ground surface and a waisted tubular envelope consisting of a continuous membrane having an unbroken surface of saddle shape and made of a material which is capable of supporting tension in all directions in its plane, the membrane being tensioned and carried with its tubular axis upright from the support structure. An open latticework anchors the lower border of the membrane to the ground surface and provides an inlet for entry of cooling air into the interior of the membrane, said membrane having an open upper end serving as an air outlet opening and a ring connected to the upper border of the membrane and to the support structure with the envelope stretched in an axial direction between its upper and lower borders, and with the support structure providing the vertical component of the tensioning. The support structure is of sufficient strength to support the membrane in a sufficiently stretched condition to cause the tensioning to create tensile forces in the membrane in all directions in the plane of the waisted envelope, with the tensile forces being greater than the compression forces created by the wind externally to the shell.</p>
