  We perform Glauber model calculations of the antiproton-nucleus elastic and
quasielastic scattering and absorption in the beam momentum range $\sim
0.5\div10$ GeV/c. A good agreement of our calculations with available LEAR data
and with earlier Glauber model studies of the $\bar p A$ elastic scattering
allows us to make predictions at the beam momenta of $\sim 10$ GeV/c, i.e. at
the regime of the PANDA experiment at FAIR. The comparison with the
proton-nucleus elastic scattering cross sections shows that the diffractive
minima are much deeper in the $\bar p A$ case due to smaller absolute value of
the ratio of the real-to-imaginary part of the elementary elastic amplitude.
Significant polarization signal for $\bar p A$ elastic scattering at 10 GeV/c
is expected. We have also revealed a strong dependence of the $\bar p A$
absorption cross section on the slope parameter of the transverse momentum
dependence of the elementary $\bar pN$ amplitude. The $\bar p A$ optical
potential is discussed.
