  On the basis of recently computed nonlinear convective pulsation models of
Galactic Cepheids, spanning wide ranges of input stellar parameters, we derive
theoretical mass-dependent Period-Wesenheit relations in the Gaia bands, namely
$G$, $G_{BP}$ and $G_{RP}$, that are found to be almost independent of the
assumed efficiency of super-adiabatic convection. The application to a selected
sub-sample of Gaia Data Release 2 Galactic Cepheids database allows us to
derive mass-dependent estimates of their individual distances. By imposing
their match with the astrometric values inferred from Gaia, we are able to
evaluate the individual mass of each pulsator. The inferred mass distribution
is peaked around 5.6$M_{\odot}$ and 5.4$M_{\odot}$ for the F and FO pulsators,
respectively. If the estimated Gaia parallax offset $<\Delta\varpi>$=0.046 mas
is applied to Gaia parallaxes before imposing their coincidence with the
theoretical ones, the inferred mass distribution is found to shift towards
lower masses, namely $\sim$5.2$M_{\odot}$ and 5.1$M_{\odot}$ for the F and FO
pulsators, respectively. The comparison with independent evaluations of the
stellar masses, for a subset of binary Cepheids in our sample, seems to support
the predictive capability of current theoretical scenario. By forcing the
coincidence of our mass determinations with these literature values we derive
an independent estimate of the mean offset to be applied to Gaia DR2
parallaxes, $<\Delta\varpi>$=0.053 $\pm$ 0.029 mas, slightly higher but in
agreement within the errors with Riess2018 value.
