  We study the three body lepton flavor violating (LFV) decays $\mu^- \to e^-
e^+ e^-$, $\tau^- \to l_i^- l_j^+ l_j^-$ and the semileptonic decay $\tau \to
\mu \phi $ in the flavor changing neutral current (FCNC) mediated $Z$ boson
model. We also calculate the branching ratios for LFV leptonic B decays,
$B_{d,s} \to \mu e$, $B_{d,s} \to \tau e$, $B_{d,s} \to \tau \mu$ and the
conversion of muon to electron in Ti nucleus. The new physics parameter space
is constrained by using the experimental limits on $\mu^- \to e^- e^+ e^-$ and
$\tau^- \to \mu^- \mu^+ \mu^-$. We find that the branching ratios for $\tau \to
eee $ and $\tau \to \mu \phi$ processes could be as large as $\sim {\cal
O}(10^{-8})$ and ${\rm Br}B_{d,s} \to \tau \mu, \tau e) \sim {\cal
O}(10^{-10})$. For other LFV B decays the branching ratios are found to be too
small to be observed in the near future.
