This paper presents the modeling of the F9 V star beta Virginis based on seismological measurements. Using the Geneva evolution code including rotation and atomic diffusion, we find that two distinct solutions reproduce all existing asteroseismic and non-asteroseismic observational constraints well: a main-sequence model with a mass of 1.28 +/- 0.03 M-. and an age t = 3.24 +/- 0.20 Gyr, or a model in the post-main sequence phase of evolution with a lower mass of 1.21 +/- 0.02 M-. and an age t = 4.01 +/- 0.30 Gyr. The small spacings delta gamma(02) and the ratio r(02) between small and large spacings are sensitive to the differences in the structure of the central layers between these two solutions and are also sensitive to the structural changes due to the rotational mixing. They can therefore be used to unambiguously determine the evolutionary state of beta Vir and to study the effects of rotation on the inner structure of the star. Unfortunately, existing asteroseismic data do not enable such precise determination. We also show that the scatter in frequencies introduced by the rotational splittings can account for the larger dispersion of the observed large spacings for the non-radial modes than for the radial modes.