We use Density Functional Theory to study the effects on the crystal structure and the electronic band structure of substituting Pb for Bi in Bi2Sr2Ca2Cu3O10. We further use the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA). The Virtual Crystal Approximation (VCA) was used to account for the substitution. We found that GGA reproduces better the lattice parameters although in both cases the internal coordinates were reproduced with some uncertainties. We further looked at the behavior of the so called Bi–O pockets, some electronic states that originate on the Bi–O planes and that appear on the Fermi surface (FS) in contradiction to the experimental evidence. We found that LDA and GGA differ on that subject. With 26% Pb and using LDA, the Bi–O pockets run away from the FS. But when GGA is used, it is needed up to 35% Pb to make the Bi–O pockets disappear from the FS. In the last case, once the Bi–O pockets are removed from the FS, we get a very good agreement with angular resolved photo-emission (ARPES) and nuclear magnetic resonance (NMR) experiments.