Accurate antiproton-nucleus elastic scattering angular distributions measured at two incident energies,∼50 and ∼180 MeV, on 12C, 40Ca, 208Pb and at 178.4 MeV on 16,18O have been analysed in the framework of the optical model. Extensive searches on the relative sensitivities to the different potential parameters have been done. Optical potentials with charge-distribution geometries failed in reproducing the experimental data; the finite range of the interaction has to be taken into account. The corresponding optical potentials have shallow real parts 5 MeV ≤ V0 ≤ 105 MeV, their imaginary depths are at least twice larger than their real depths. These features rule out some models but are consistent with an analysis of recent p-atom data. The sensitivity of the optical-model analysis of elastic scattering data to the details of the radial potential has been investigated. Target mass and energy evolution of the strong-absorption radius and reaction cross section confirm that the antiproton penetrates more inside the target nucleus when the incident energy increases. Some features of the phenomenological potentials are compared with the predictions of microscopic potentials.