  The $\Lambda$- and $\Xi^-$-hyperon mean free paths in nuclei are firstly
calculated in the relativistic mean field (RMF) theory. The real parts of the
optical potential are derived from the RMF approach, while the imaginary parts
are obtained from those of nucleons with the relations:
$U^{\mathrm{IY}}_{\mathrm{S}} = \alpha_{\sigma \mathrm{Y}}\cdot
U_{\mathrm{S}}^{\mathrm{IN}}$ and $U^{\mathrm{IY}}_{\mathrm{V}} =
\alpha_{\omega \mathrm{Y}}\cdot U_{\mathrm{V}}^{\mathrm{IN}}$ . With the
assumption, the depth of the imaginary potential for $\Xi^-$ is
$W_{\Xi}\simeq-$ 3.5 MeV, and for $\Lambda$ is $W_{\Lambda}\simeq-$ 7 MeV at
low incident energy. We find that, the hyperon mean free path decreases with
the increase of the hyperon incident energies, from 200 MeV to 800 MeV; and in
the interior of the nuclei, the mean free path is about $2\sim 3$ fm for
$\Lambda$, and about $4\sim 8$ fm for $\Xi^-$, depending on the hyperon
incident energy.
