We study Lepton Flavour Violating hadron decays of the tau lepton within the Simplest Little Higgs model. Namely we consider $tau rightarrow mu (P, V, PP)$ where $P$ and $V$ are short for a pseudoscalar and a vector meson. We find that, in the most positive scenarios, branching ratios for these processes are predicted to be, at least, four orders of magnitude smaller than present experimental bounds.