  Context: It is well known that the so-called s-process is responsible for the
production of neutron-rich trans-iron elements, that form the bulk of the
"heavy nuclides" (i.e. nuclides more massive than the iron-group nuclei) in the
solar-system composition, considered as "standard of reference" dataset for
cosmic abundances. In particular, the s-process produces about half of all the
trans-iron isotopes by moving along the "valley of stability" through a series
of neutron capture reactions and beta decays. More than one s-process
"component" (i.e. a nucleosynthesis event with a single set of physical
conditions like neutron exposure, initial abundances and neutron density) is
required in order to explain the observed solar distribution of s-nuclei
abundances. Current views on the subject suggest the existence of several
components that, in terms of stellar environments, correspond to distinct
categories of stars in different evolutionary phases. Aims: The purpose of the
chapter is to review the s-process nucleosynthesis occurring in massive stars
(so-called weak component of s-process), pointing particular attention on the
recent studies devoted to analyze how the uncertainties due to stellar
evolution modeling and, specifically, due to convective overshooting affect the
efficiency of this nucleosynthesis process.
