Experimental data on the volume changes accompanying simple tension of peroxide vulcanizates of natural gum rubber, as first reported by Penn in Trans. Soc. Rheol., 14, 509 (1970), are further interpreted within the framework of the theory of a hyperelastic material. Motivated by the formal connection between a hyperelastic material and a nonlinear viscoelastic fluid (Trans. Soc. Rheol., 9, 27 (1965)), and a mathematical result on the decomposition of the scalar potential of that fluid (Z. Angew. Math. Phys. 23, 780 (1972)), the interpretation of Penn's data leads to an explicit construction of a strain‐energy function for rubbery materials: W(I 1 ,I 2 ,I 3 )=C 1 (I 1 −3)+C 2 (I 2 −3)+H̄(I 1 ,I 2 )(I 3 −1)+ 1 8K (I 3 −1) 2 .