  We study constraints on new physics from the recent measurement of Br ($K^+
\to \pi^+ \nu \bar \nu)$ by the E787 and E949 Collaborations. In our analysis
we consider two models of new physics: $(a)$ extra down type singlet quark
model (EDSQ) and $(b)$ R-parity violating Minimal Supersymmetric Standard
Model(MSSM). We find that $K^+\to \pi^+ \nu\bar \nu$ along with other processes
like $K_L \to \mu^+ \mu^-, \epsilon^\prime/\epsilon $ provide useful bounds on
the parameter $U_{sd}$, characterizing the off-diagonal $Z-d-\bar s $ coupling
of model $(a)$. The bounds on the ${\rm Re}(U_{sd})$ from $(K_L \to
\mu^+\mu^-)_{\rm SD}$ and ${\rm Im}(U_{sd})$ from $\epsilon^\prime/\epsilon$
are so tight that the branching ratio of $K^+\to \pi^+ \nu \bar \nu $ can
exceed the standard model value by at most a factor of two For model b), we
also obtain stringent bounds on certain combinations of product of two
$\lp_{ijk}$ couplings originating from $L$ number violating operator $ L_i Q_j
D^c_k $ using $K^+ \to \pi^+ \nu \bar \nu $ and $K_L \to \mu^+ \mu^-$
processes. Even with the stringent constraints on $U_{sd}$ (in model $(a)$) and
on products of two $\rp$couplings (model $(b)$), we find that the branching
ratios for $K_L \to \pi^0 \nu \bar \nu$ and $K_L \to \pi^0 e^+ e^-$ can be
substantially different in both the above models from those predicted in the
standard model.
