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. A good agreement of our calculations with available LEAR data and with earlier Glauber model studies of thepA 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 thepA case due to smaller absolute value of the ratio of the real-to-imaginary part of the elementary elastic amplitude. Significant polarization signal forpA elastic scattering at 10 GeV/c is expected. We have also revealed a strong dependence of thepA absorption cross section on the slope parameter of the transverse momentum dependence of the elementarypN amplitude. ThepA optical potential is discussed.