  The existence of static, self-gravitating elastic bodies in the non-linear
theory of elasticity is established. Equilibrium configurations of
self-gravitating elastic bodies close to the reference configuration have been
constructed in [6] using the implicit function theorem. In contrast, the steady
states considered in this article correspond to deformations of the relaxed
state with no size restriction and are obtained as minimizers of the energy
functional of the elastic body.
