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 value .