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
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