  By using the scaling method and the Thomas-Fermi and Extended Thomas-Fermi
approaches to Relativistic Mean Field Theory the surface contribution to the
leptodermous expansion of the finite nuclei incompressibility has been
self-consistently computed. The validity of the simplest expansion, which
contains volume, volume-symmetry, surface and Coulomb terms, is examined by
comparing it with self-consistent results of the finite nuclei
incompressibility for some currently used non-linear sigma-omega parameter
sets. A numerical estimate of higher-order contributions to the leptodermous
expansion, namely the curvature and surface-symmetry terms, is made.
