  Cosmic-ray particles with ultra-high energies (above $10^{18}$ eV) are
studied through the properties of extensive air showers which they initiate in
the atmosphere. The Pierre Auger Observatory detects these showers with
unprecedented exposure and precision and the collected data are processed via
dedicated software codes. Monte Carlo simulations of extensive air showers are
very computationally expensive, especially at the highest energies and
calculations are performed on the GRID for this purpose. The processing of
measured and simulated data is described, together with a brief list of physics
results which have been achieved.
