Studies on ATLAS muon efficiency measurement with Z->mu mu

The measurement of the single W and Z inclusive cross-sections is one of the main tasks of the LHC starting period. To obtain a measurement of these cross-sections with small uncertainty, the overall efficiencies for the detection of leptons have to be determined directly from data. We present a possible strategy of the ATLAS experiment to get the muon trigger and reconstruction efficiencies directly from data applying the so called Tag and Probe method to Z --> mu+mu- and other kinds of events. A complete study on Montecarlo samples is presented.