We investigate the evolution of the abundance of fluorine in the Milky Way thick and thin discs by means of detailed chemical evolution models compared with recent observational data. The chemical evolution models adopted here have already been shown to fit the observed abundance patterns of CNO and α-elements as well as the metallicity distribution functions for the Galactic thick and thin disc stars. We apply them here to the study of the origin and evolution of fluorine, which is still a matter of debate. First, we study the importance of the various sites proposed for the production of fluorine. Then, we apply the reference models to follow the evolution of the two different Galactic components. We conclude that rotating massive stars are important producers of F and they can set a plateau in F abundance below [Fe/H] = -0.5 dex, though its existence for [Fe/H]<-1 has yet to be confirmed by extensive observations of halo stars. In order to reproduce the F abundance increase in the discs at late times, instead, a contribution from lower mass stars - single asymptotic giant branch stars and/or novae - is required. The dichotomy between the thick and thin discs is more evident in the [F/O] versus [O/H] plot than in the [F/Fe] versus [Fe/H] one, and we confirm that the thick disc has evolved much faster than the thin disc, in agreement with findings from the abundance patterns of other chemical elements.
