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 .