  We investigate the interior Einstein's equations in the case of a static,
axially symmetric, perfect fluid source. We present a particular line element
that is specially suitable for the investigation of this type of interior
gravitational fields. Assuming that the deviation from spherically symmetry is
small, we linearize the corresponding field equations and find several classes
of vacuum and perfect fluid solutions. We find physically meaninful spacetimes
by imposing appropriate matching conditions.
