  The isospin dependence of incompressibility is investigated in the Skyrme
Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations
between the nuclear matter incompressibility and the isospin dependent term of
the finite nucleus incompressibility is elucidated by using the Thomas-Fermi
approximation. The Coulomb term is also studied by using various different
Skyrme
  Hamiltonians and RMF Lagrangians. The symmetry energy coefficient of
incompressibility is extracted to be K_{\tau}=-(500\pm50) MeV from the recent
experimental data of isoscalar giant monopole resonances (ISGMR) in Sn
isotopes. Microscopic HF+random phase approximation (RPA) calculations are also
performed with Skyrme interactions for ^{208}Pb and Sn isotopes to study the
strength distributions of ISGMR. .
