  The shift of atomic energy levels due to hadronic vacuum polarization is
evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen.
A parametric hadronic polarization function obtained from experimental cross
sections of $e^-e^+$ annihilation into hadrons is applied to derive an
effective relativistic Uehling potential. The energy corrections originating
from hadronic vacuum polarization are calculated for low-lying levels using
analytical Dirac-Coulomb wave functions, as well as bound wave functions
accounting for the finite nuclear size. Closed formulas for the hadronic
Uehling potential of an extended nucleus as well as for the relativistic energy
shift in case of a point-like nucleus are derived. These results are compared
to existing analytic formulas from non-relativistic theory.
