We perform Glauber model calculations of the antiproton–nucleus elastic and quasielastic scattering and absorption in the beam momentum range ∼0.5÷10 GeV/c∼0.5÷10 GeV/c. A good agreement of our calculations with available LEAR data and with earlier Glauber model studies of the p¯A elastic scattering allows us to make predictions at the beam momenta of ∼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 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 p¯A elastic scattering at 10 GeV/c is expected. We have also revealed a strong dependence of the p¯A absorption cross section on the slope parameter of the transverse momentum dependence of the elementary p¯N amplitude. The p¯A optical potential is discussed.