  The sensitivity of the atmospheric neutrino experiments to the non-standard
flavor-dependent interaction in neutrino propagation is studied under the
assumption that the only nonvanishing components of the non-standard matter
effect are the electron and tau neutrino components $\epsilon_{ee}$,
$\epsilon_{e\tau}$, $\epsilon_{\tau\tau}$ and that the tau-tau component
satisfies the constraint
$\epsilon_{\tau\tau}=|\epsilon_{e\tau}|^2/(1+\epsilon_{ee})$ which is suggested
from the high energy behavior for atmospheric neutrino data. It is shown that
the Superkamiokande (SK) data for 4438 days constrains
$|\tan\beta|\equiv|\epsilon_{e\tau}/(1+\epsilon_{ee})|\lesssim 0.8$ at
2.5$\sigma$ (98.8\%) CL whereas the future Hyperkamiokande experiment for the
same period of time as SK will constrain as $|\tan\beta|\lesssim 0.3$ at
2.5$\sigma$CL from the energy rate analysis and the energy spectrum analysis
will give even tighter bounds on $\epsilon_{ee}$ and $|\epsilon_{e\tau}|$.
