  The spin filtering by a multiple passage of a stored beam through a polarized
internal gas target is a unique possibility of polarizing high luminosity beam
of antiprotons to a high degree of polarization. Apart from the polarization by
the spin-dependent transmission, a unique geometrical feature of spin filtering
in storage rings is a scattering of stored particles within the ring
\cite{Meyer}. A rotation of the spin in the scattering process affects the
polarization buildup. We report here a fully quantum-mechanical evolution
equation for the spin-density matrix of a stored beam which incorporates the
scattering within the ring. We show how dramatically the interplay of the
transmission and scattering within the ring changes from polarized electrons to
polarized protons in the atomic target. After discussions of the FILTEX results
on filtering of stored protons \cite{FILTEX}, we comment on the strategy of
spin filtering of antiprotons for the PAX experiment at GSI FAIR \cite{PAX-TP}.
