  This article presents the sensitivity of the ATLAS experiment to the
lepton-flavour-violating decays of $\tau\to 3\mu$. A method utilising the
production of $\tau$ leptons via $W\to\tau\nu$ 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, ${\rm Br}(\tau\to 3\mu)$, is $3.76\times 10^{-7}$ ($3.94\times 10^{-7}$)
at 90% confidence level.
