  The usefulness of the three-body mechanism of $\eta$-meson production is
tested by extending to high energies a recently developed two step model of the
$p d \to ^3$He $\eta$ reaction by us, which was successful in reproducing the
energy dependence of the data near threshold. The $\eta$ production in this
model, proceeds in two steps via the $p p \to \pi d$ and $\pi N \to \eta p$
reactions with the intermediate particles being off-shell. The final state
interaction(FSI) is incorporated through a $T$-matrix for $\eta^3$He elastic
scattering constructed using few body equations. In a comparison of the
calculated angular distributions with some recently available data, we discover
the limitations of the model at high energies.
