2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93424We present a calculation scheme for the two-loop vacuum polarization correction of order $α^2$ to the Lamb shift of hydrogen-like high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in $(Zα)$. By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogen-like Lead and Uranium are presented.23 pages, LaTeX (RevTeX), 5 eps-figuresQuantum Physicstext