This article presents the sensitivity of the ATLAS experiment to the lepton-flavour-violating decays of $$\tau \rightarrow 3\mu $$ . A method utilising the production of $$\tau $$ leptons via $$W\rightarrow \tau \nu $$ decays is used. This method is applied to the sample of 20.3 fb $$^{-1}$$ of pp collision data at a centre-of-mass energy of 8 TeV collected by the ATLAS experiment at the LHC in 2012. No event is observed passing the selection criteria, and the observed (expected) upper limit on the $$\tau $$ lepton branching fraction into three muons, $$\mathrm{Br}(\tau \rightarrow 3\mu )$$ , is $$3.76\times 10^{-7}$$ ( $$3.94\times 10^{-7}$$ ) at 90 % confidence level.