The multistring model VENUS has been applied in the calculation of antiproton and antineutron yields and longitudinal momentum (Feynman Xf) spectra for p-p, p-Pb, O-Pb, and Si-Si collisions at 200A and 1000A GeV incident nuclear energies. The antiproton spectra of p-Cu collisions at an incident proton energy of 120 GeV are also analysed. The calculated antiproton spectra in the small Xf region are smaller than those calculated by Hojovat and Van-Ginneken's empirical formula used in the design of the Fermilab Tevatron antiproton source. In contrast to previous theoretical calculations, the antiproton spectra calculated by VENUS do not show asymptotic behaviour for an incident nucleon energy of 200-1000 GeV caused by the large mass of antiprotons. The yield and spectra of the antineutrons is very close to that of the antiprotons in all of the cases studied. The pion yield in a 200 GeV per nucleon energy O-Pb collision calculated by the VENUS code can explain the difference between the experimental and the calculated values for non-central collisions.