Detailed models of Procyon A based on new asteroseismic measurements by Eggenberger et al. (2004b) have been computed using the Geneva evolution code including shellular rotation and atomic diffusion. By combining all non-asteroseismic observables now available for Procyon A with these seismological data, we find that the observed mean large spacing of 55.5 +/- 0.5 muHz favours a mass of 1.497M(circle dot) for Procyon A. We also determine the following global parameters of Procyon A: an age of t = 1.72 +/- 0.30 Gyr, an initial helium mass fraction Y-i = 0.290 +/- 0.010, a nearly solar initial metallicity (Z/X)(i) = 0.0234 +/- 0.0015 and a mixing-length parameter alpha = 1.75 +/- 0.40. Moreover, we show that the effects of rotation on the inner structure of the star may be revealed by asteroseismic observations if frequencies can be determined with a high precision. Existing seismological data of Procyon A are unfortunately not accurate enough to really test these differences in the input physics of our models. (C) 2004 Elsevier B.V. All rights reserved.