  The properties of nuclear matter are studied in the cut-off field theory. It
is found that, under the Hartree approximation, the small cut-off makes the
equations of state hard, especially at higher densities. The theory is modified
in the framework of the renormalization group methods with arbitrary cut-off
$\Lambda^\prime$. It is found that the expansion in terms of the $\sigma$ meson
field is more favorable than the naive expansion of the inverse of
$\Lambda^\prime$, when we do not use very large $\Lambda^\prime$.
