  We consider the problem of a scalar field, non-minimally coupled to gravity
through a $-\xi\phi^{2}R$ term, in the presence of a Brane. Exact solutions,
for a wide range of values of the coupling parameter $\xi$, for both
$\phi$-dependent and $\phi$-independent Brane tension, are derived and their
behaviour is studied. In the case of a Randall-Sundrum geometry, a class of the
resulting scalar field solutions exhibits a folded-kink profile. We go beyond
the Randall-Sundrum geometry studying general warp factor solutions in the
presence of a kink scalar. Analytic and numerical results are provided for the
case of a Brane or for smooth geometries, where the scalar field acts as a
thick Brane. It is shown that finite geometries with warp factors that
asymptotically decrease exponentially are realizable for a wide range of
parameter values. We also study graviton localization in our setup and find
that the localizing potential for gravitons with the characteristic
volcano-like profile develops a local maximum located at the origin for high
values of the coupling $\xi$.
