The tensile structure 

is the most common type of thin shell structure. Most tensile structures are supported by some form of compression or bending element.

tensile membrane structure is most often used as a roof, as they can economically and attractively span large distances. Tensile membrane structures may also be used as complete buildings, with a few common applications being sports facilities, warehousing and storage buildings, and exhibition venues.Common materials for doubly curved fabric structures are PTFE-coated fiberglass and PVC-coated polyester. These are woven materials with different strengths in different directions.

Air-supported structures are a form of tensile structures where the fabric envelope is supported by pressurised air only.

The majority of fabric structures derive their strength from their doubly curved shape. By forcing the fabric to take on double-curvature the fabric gains sufficient stiffness to withstand the loads it is subjected to (for example wind and snow loads). In order to induce an adequately doubly curved form it is most often necessary to pretension or prestress the fabric or its supporting structure