The energy is among the characteristics of Ultra High Energy Cosmic Rays (E>5 x 10^19 eV) which could be estimated experimentally and by simulations. The following paper attempts to estimate the energy of an UHECR proton by applying a Monte Carlo simulation code. A number of extensive air showers, vertical and inclined, is simulated to derive the muon density as a function of radial distance from the core of the shower. This scenario of simulations could be applied to the Cerenkov surface detector of the P. AUGER Observatory as well. Due to the fact that this density shows minimal fluctuations at a distance larger than 900 m from the core of the showers and that at the same distance the muon density for inclined showers coincide, we select this favorable distance to derive the energy of such high energy protons. The project is co-funded by the European Social Fund and National Resources (EPEAEK II) PYTHAGORAS II.