Abstract: A search for charged lepton flavour violation in tau -> 3 μdecays is performed in pp collisions at a centre-of-mass energy of 13 TeV using ATLAS data collected between 2016 and 2018, corresponding to an integrated luminosity of 137 fb(-1). The search is optimised for the electroweak W -> tau nu production channel, due to its higher trigger efficiency, but also considers potential signal events from heavy-flavour production. Data are collected using two-muon and three-muon triggers and a multivariate analysis is used to separate the signal from the background. An unbinned likelihood fit is then performed to the resulting three-muon invariant mass spectrum and the data are found to be compatible with the background-only hypothesis. The observed (expected) limit on the branching ratio B(tau -> 3 mu) is found to be 8.7 x 10(-8) (7.5 x 10(-8)) at 90% CL