© CERN 2015 for the benefit of the ATLAS collaboration. This paper describes the concept, technical realisation and validation of a largely data-driven method to model events with Zττ decays. In Zμμ events selected from proton-proton collision data recorded at s=8 TeV with the ATLAS experiment at the LHC in 2012,the Z decay muons are replaced by τ leptons from simulated Zarrowττ decays at the level of reconstructed tracks and calorimeter cells. The τ lepton kinematics are derived from the kinematics of the original muons. Thus, only the well-understood decays of the Z boson and τ leptons as well as the detector response to the τ decay products are obtained from simulation. All other aspects of the event, such as the Z boson and jet kinematics as well as effects from multiple interactions, are given by the actual data. This so-called τ-embedding method is particularly relevant for Higgs boson searches and analyses in ττ final states, where Zarrowττ decays constitute a large irreducible background that cannot be obtained directly from data control samples. In this paper, the relevant concepts are discussed based on the implementation used in the ATLAS Standard Model Hττ analysis of the full datataset recorded during 2011 and 2012.