  We have investigated the role of the convective overshooting on the
production of s-nuclei during core He-burning phase in stellar models with
different initial mass and metallicity ($15 \leq M_{ZAMS}/M_{\odot} \leq 25$;
$10^{-4} \leq Z \leq 0.02$), considering a diffusive approach to model the
convective overshooting. The results and their possible consequences on some
open questions linked to the s-process weak component efficiency are discussed.
