We present a detailed study of s-process nucleosynthesis in massive stars of solar-like initial composition and masses 15, 20, 25, and 30 M-circle dot. We update our previous results of s-process nucleosynthesis during the core He burning of these stars and then focus on an analysis of the s-process under the physical conditions encountered during the shell carbon burning. We show that the recent compilation of the Ne-22(alpha; n)(25) Mg rate leads to a remarkable reduction of the efficiency of the s-process during core He burning. In particular, this rate leads to the lowest overproduction factor of Kr-80 found to date during core He burning in massive stars. The s-process yields resulting from shell carbon burning turn out to be very sensitive to the structural evolution of the carbon shell. This structure is influenced by the mass fraction of C-12 attained at the end of core helium burning, which in turn is mainly determined by the C-12(alpha; gamma) O-16 reaction. The still- present uncertainty in the rate for this reaction implies that the s-process in massive stars is also subject to this uncertainty. We identify some isotopes like Zn-70 and Rb-87 as the signatures of the s-process during shell carbon burning inmassive stars. In determining the relative contribution of our s-only stellar yields to the solar abundances, we find it is important to take into account the neutron exposure of shell carbon burning. When we analyze our yields with a Salpeter initial mass function, we find that massive stars contribute at least 40% to s-only nuclei with mass A <= 87. For s-only nuclei with mass A > 90, massive stars contribute on average similar to 7%, except for Gd-152, Os-187, and Hg-198, which contribute similar to 14%, similar to 13%, and similar to 11%, respectively.