We present a combined fit of a simple astrophysical model of UHECR sources to both the energy spectrum and mass composition data measured by the Pierre Auger Observatory. The fit has been performed for energies above 5 ⋅ 1018 eV, i.e. the region of the all-particle spectrum above the so-called "ankle" feature. The astrophysical model we adopted consists of identical sources uniformly distributed in a comoving volume, where nuclei are accelerated through a rigidity-dependent mechanism. The fit results suggest sources characterized by relatively low maximum injection energies, hard spectra and heavy chemical composition. We also show that uncertainties about physical quantities relevant to UHECR propagation and shower development have a non-negligible impact on the fit results.