  The $\eta$-3N-interaction is studied within the four-body Faddeev-Yakubovsky
theory adopting purely separable forms for the two- and three-body
subamplitudes, limiting the basic two-body interactions to s-waves only. The
corresponding separable approximation for the integral kernels is obtained by
using the Hilbert-Schmidt procedure. Results are presented for the $\eta$-$^3$H
scattering amplitude and for the total elastic cross section for energies below
the triton break-up threshold.
