  The s-process, a production mechanism based on slow-neutron capture during
stellar evolution, is the origin of about half the elements heavier than iron.
Abundance predictions for s-process nucleosynthesis depend strongly on the
relevant neutron-capture and $\beta$-decay rates, as well as on the details of
the stellar model being considered. Here, we have used a Monte-Carlo approach
to evaluate the nuclear uncertainty in s-process nucleosynthesis. We considered
the helium burning of massive stars for the weak s-process and low-mass
asymptotic-giant-branch stars for the main s-process. Our calculations include
a realistic and general prescription for the temperature dependent uncertainty
for the reaction cross sections. We find that the adopted uncertainty for
(${\rm n},\gamma$) rates, tens of per cent on average, effects the production
of s-process nuclei along the line of $\beta$-stability, and that the
uncertainties in $\beta$-decay from excited state contributions, has the
strongest impact on branching points.
