  We prove existence of solutions for an elastic body interacting with itself
through its Newtonian gravitational field. Our construction works for
configurations near one given by a self-gravitating ball of perfect fluid. We
use an implicit function argument. In so doing we have to revisit some
classical work in the astrophysical literature concerning linear stability of
perfect fluid stars. The results presented here extend previous work by the
authors, which was restricted to the astrophysically insignificant situation of
configurations near one of vanishing stress. In particular, "mountains on
neutron stars", which are made possible by the presence of an elastic crust in
neutron stars, can be treated using the techniques developed here.
