Detailed models of Procyon A based on new asteroseismic measurements by Eggenberger et al (2004) 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 uHz favours a mass of 1.497 M_sol 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.