  The lepton flavor violation $\mu\to e\gamma$, $\tau\to e\gamma$,
$\tau\to\mu\gamma$, $\mu\to3e$, $\tau\to3e$, $\tau\to3\mu$ and $\mu-e$
conversion in Al and Ti are studied in both the Altarelli-Feruglio $A_4$ model
and the $S_4$ model of Ding. The rates of these lepton flavor violation process
for the inverted hierarchy neutrino mass spectrum are enhanced considerably by
the next to leading order contributions. For both models, we find that the
$\mu-e$ conversion in Ti is within the precision of next generation experiments
in all the parameter space considered, the $\mu-e$ conversion in Al should be
observable at least in a very significant part of the parameter space, whereas
$\tau\to e\gamma$, $\tau\to\mu\gamma$, $\tau\to3e$ and $\tau\to3\mu$ are below
the expected future sensitivity. The detectability of $\mu\to e\gamma$ and
$\mu\to3e$ in near future depends on the models and the neutrino mass spectrum.
We suggest that a comprehensive consideration of the lepton flavor violation
processes is important to test and distinguish both discrete flavor symmetry
models.
