The response of textile materials to transverse compression is of great importance in many applications. In this paper is discussed the mechanical properties of textile materials when subjected to transverse compression. The response of a textile to load is very non-linear and inelastic. The response is viscoelastic (there are rate effects) and plastic (there are permanent deformations). It is shown that energy is stored in a textile when it is loaded, and that some of this energy is not released when the material is unloaded, but instead is locked into its structure. This locked energy cannot be released unless the structure is placed in tension. A thermomechanical framework is introduced which incorporates the textile locked energy. Models are developed which predict well the response of textiles to load.