In this paper there is introduced a strain energy function which describes a class of materials that includes elastic animal tissue as well as other highly distensible materials. The functional form of this representation is general enough to suggest other forms that may encompass additional classes of material. The theoretical stress‐strain curves are shown to correlate well with experimental data obtained upon loading (as distinguished from unloading) different animal tissues such as frog’s striated muscle, human papillary muscle, and cat’s and rabbit’s mesentery, as well as synthetic materials such as latex rubber. There is also developed a thinness theory which can be used to calculate the deformation field in the case of applied plane stress for the more complicated geometry of a wedge‐shaped (arcuate) specimen. This thinness theory has been applied to a fan‐shaped specimen with tangential and radial loading.