  An explicit necessary condition for the occurrence of resonance scattering of
axial gravitational waves, along with the internal trapping of null geodesics,
is proposed for static spherically symmetric perfect fluid solutions to
Einstein's equations. Some exact inhomogeneous solutions which exhibit this
trapping are given with special attention to boundary conditions and the
physical acceptability of the space times. In terms of the tenuity ($\alpha =
R/M$ at the boundary) all the examples given lie in the narrow range $2.8 <
\alpha < 2.9$. The tenuity can be raised to more interesting values by the
addition of an envelope without altering the trapping.
