  We study properties of domain walls in the symmetron model, in which the
scalar gravitational degree of freedom decouples from matter in regions of high
density, and exhibits a spontaneously broken $Z_2$ symmetry at low densities.
The non-minimal coupling of the scalar to matter leads to a host of interesting
properties of the domain walls that are not present in minimally coupled
theories. We estimate the cosmological energy fraction in domain walls and find
that this leads to an upper bound on the redshift of the symmetry breaking. We
also show that a spherical symmetron wall can remain stable if it is "pinned"
on matter halos and derive a criterion for the stability. In addition, we
present results of numerical simulations of representative interactions between
domain walls and matter over-densities.
