  We present a theoretical study of spin polarized transport in Fe atomic
contacts using a self-consistent tight-binding Hamiltonian in a non-orthogonal
$s$, $p$ and $d$ basis set, the spin-polarization being obtained from a
non-collinear Stoner-like model and the transmission probability from the
Fisher-Lee formula. The behaviour of an infinite perfect Fe wire is compared
with that of an infinite chain presenting geometric defects or magnetic walls
and with that of a finite chain connected to infinite one-dimensional or
three-dimensional leads. In the presence of defects or contacts the
transmission probability of $d$ electrons is much more affected than that of
$s$ electrons, in particular, contact effects may suppress some transmission
channels. It is shown that the behaviour of an infinite wire is never obtained
even in the limit of long chains connected to electrodes. The introduction of
the spin-orbit coupling term in the Hamiltonian enables us to calculate the
anisotropy of the magneto-resistance. Finally whereas the variation of the
magneto-resistance as a function of the magnetization direction is step-like
for an infinite wire, it becomes smooth in the presence of defects or contacts.
