  Flavor changing neutral current processes such as $b \to s \gamma$, $b \to s
l^+ l^-$, $b \to s \nu \bar{\nu}$, $\epsilon_K$, $\Delta m_B$, $K^+ \to \pi^+
\nu \bar{\nu}$ and $\K_L \to \pi^0 \nu \bar{\nu}$ are calculated in the
supersymmetric standard model based on supergravity. We consider two
assumptions for the soft supersymmetry breaking terms. In the minimal case soft
breaking terms for all scalar fields are taken to be universal at the GUT scale
whereas those terms are different for the squark/slepton sector and the Higgs
sector in the nonminimal case. In the calculation we have taken into account
the next-to-leading order QCD correction to the $b \to s \gamma$ branching
ratio, the results from the LEP II superparticles search, and the condition of
the radiative electroweak symmetry breaking. We show that $\Delta m_B$ and
$\epsilon_K$ can be enhanced up to 40% compared to the Standard Model values in
the nonminimal case. In the same parameter region the $b \to s \nu \bar{\nu}$,
$K^+ \to \pi^+ \nu \bar{\nu}$ and $\K_L \to \pi^0 \nu \bar{\nu}$ branching
ratios are reduced up to 10%. The corresponding deviation in the minimal case
is 20% for $\Delta m_B$ and $\epsilon_K$ and within 3% for the $b \to s \nu
\bar{\nu}$, $K^+ \to \pi^+ \nu \bar{\nu}$ and $\K_L \to \pi^0 \nu \bar{\nu}$.
For the $b \to s l^+ l^-$ process the significant deviation from the Standard
Model is realized only when the $b \to s \gamma$ amplitude has an opposite sign
to the Standard Model prediction. Significance on these results from possible
future improvements of the $b \to s \gamma$ branching ratio measurement and top
squark search is discussed.
