Abstract : Secondary atmospheric antiprotons are studied. A parametrisation of the inclusive cross section for the pbar production in p+p and p+A collisions is developed, based on the Quark Counting Rule, the Regge Phenomenology and data fitting. This parametrisation is shown to have a good agreement with experimental data for incident nucleon energy at least up to 24 GeV/n in the laboratory frame. By the analysis of the pbar mean multiplicity distribution, this parametrisation can extend at least up to the centre of mass energy s^1/2 about 25 GeV. Based on this well developed parametrisation, the Wounded Nucleon Model is applied to obtained the pbar production cross section in A+A collisions. By including cosmic protons and heliums, the atmospheric pbar flux at high balloon and satellite altitudes are calculated. The He-induced collisions are shown to contribute about 30 % in the total secondary atmospheric pbar flux. It is observed that, for the interest of the pbar exotic origins such as the annihilation of supersymmetric dark matter (neutralino) and the evaporation of primordial black holes, the energy range up to E=200 GeV/n for cosmic particles generating the secondary atmospheric pbar production is the most important. It is shown that the secondary atmospheric pbar flux used to correct the pbar flux at TOA was underestimated in the previous works. In this work, the pbar flux at TOA is then modified 10-15 % lower than the originally deduced, for the energy range E_k>1 GeV. A pbar measurement experiment at the ground level is used to test the accuracy of secondary atmospheric pbar production calculated by different works. The results of the BESS 1999 experiment at 2.77 km have confirmed the correctness of the present approach. At the AMS altitude, it is shown that the pbar flux measured by AMS is almost the exact pbar flux at TOA, with only 2-3 % of the atmospheric pbar component. It is found that, even at very high altitudes, thousands of kilometres above the Earth, there are still some residual atmospheric antiprotons and their trajectories are very complex and cannot be well explained by the usual variables. Finally, the secondary atmospheric p flux at low altitudes are calculated. The deviation between the calculation and the measurements and the possible origins of this deviation are discussed. Comments, remarks and conclusions are given.