The recent results of the Pierre Auger Observatory on the possible correlation of Ultra High Energy Cosmic Rays events and several nearby discrete sources could be the starting point of a new era with charged particles astronomy. In this paper we introduce a simple model to determine the effects of any local distribution of sources on the expected flux. We consider two populations of sources: faraway sources uniformly distributed and local point sources. We study the effects on the expected flux of the local distribution of sources, referring also to the set of astrophysical objects whose correlation with the Auger events is experimentally claimed.

17 pages, 13 eps figures, version accepted for publication in Astroparticle Physics