The slow neutron capture process (s-process) is responsible for the production of about half the elements beyond the Fe-peak. The production sites and the conditions under which the different components of s-process occur are relatively well established. A detailed quantitative understanding of s-process nucleosynthesis may yield light in physical processes, e.g. convection and mixing, taking place in the production sites. For this, it is important that the impact of uncertainties in the nuclear physics is well understood. In this work we perform a study of the sensitivity of s-process nucleosynthesis, with particular emphasis in the main component, on the nuclear reaction rates. Our aims are: to quantify the current uncertainties in the production factors of s-process elements originating from nuclear physics and, to identify key nuclear reactions that require more precise experimental determinations. In this work we studied two different production sites in which s-process occurs with very different neutron exposures: 1) a low-mass extremely metal-poor star during the He-core flash (nn reaching up to values of ∼ 1014cm-3); 2) the TP-AGB phase of a M , Z=0.01 model, the typical site of the main s-process component (nn up to 108 - 109cm-3). In the first case, the main variation in the production of s-process elements comes from the neutron poisons and with relative variations around 30%-50%. In the second, the neutron poison are not as important because of the higher metallicity of the star that actually acts as a seed and therefore, the final error of the abundances are much lower around 10%-25%.