  We make an evaluation of the lepton flavor violating (LFV) decays $\tau \to
\ell (V^0, P^0)$, where $\ell=e$ or $\mu$ and $V^0(P^0)$ is a neutral vector
(pseudo-scalar) meson, in the context of unparticle physics. The constraints
are investigated systematically on the related coupling parameters from all the
available experimental data, and the parameter values are specified
appropriately. The results show that whereas over the whole parameter space
allowed by experiments all the $\tau \to \ell P^0$ modes have a branching ratio
too small to be measurable experimentally, in a large subspace as observed all
of the $\tau \to \ell V^0$ modes get simultaneously a branching ratio as high
as ${\cal O}(10^{-10}-10^{-8})$, which is reachable at the LHC and super B
factory. The important implications are drawn.

High Energy Physics - Phenomenology