The observation of neutrino oscillations indicates that lepton flavour violation (LFV) occurs in nature and that lepton flavour is not an exact symmetry. However, no observation has been made in the charged sector, which would be a clear indication of physics Beyond the Standard Model (BSM). There are BSM models which predict LFV decays of the Higgs boson into a pair of leptons with different flavours such as models with more than one Higgs doublet, composite Higgs models, models with flavour symmetries, Randall–Sundrum models and many more. In this poster we present the search for Higgs Bosons decaying into a tau lepton and either an electron or a muon, using data collected by the ATLAS detector at a centre-of-mass energy of 13 TeV. The searches for H->e tau and H->mu tau decays were performed independently and in both cases, the search was split into cases where the tau lepton decayed leptonically or hadronically. Multivariate techniques were used in this search to discern the LFV signal from the SM background. The achieved results will be discussed in this poster.