Deformations are termed extreme when a volume, area, or line element shrinks to zero volume, zero area, or zero length, respectively, or, on the other hand, expands to infinite volume, infinite area, or infinite length. The authors study and prove growth conditions on the stored energy density and establish connections between them for solids, liquids, and gases. In the latter case, the stored energy tends to zero when the volume increases to infinity. The growth conditions are stated in terms of equivalent conditions on the volume, area, and length subenergies introduced into continuum mechanics by J. L. Ericksen. The results bear on the constitutive theory of elastic solids, fluids, and gases.