Abstract: The Z -> tau tau cross section is measured with the ATLAS experiment at the LHC in four different final states determined by the decay modes of the tau leptons: muon-hadron, electron-hadron, electron-muon, and muon-muon. The analysis is based on a data sample corresponding to an integrated luminosity of 36 pb(-1), at a proton-proton center-of-mass energy of root s = 7 TeV. Cross sections are measured separately for each final state in fiducial regions of high detector acceptance, as well as in the full phase space, over the mass region 66-116 GeV. The individual cross sections are combined and the product of the total Z production cross section and Z -> tau tau branching fraction is measured to be 0.97 +/- 0.07(stat) +/- 0.06(syst) +/- 0: 03(lumi) nb, in agreement with next-to-next-to-leading order calculations.