We report a study on the measurement of the SUSY breaking scale √F in the framework of gauge-mediated supersymmetry breaking (GMSB) models at the LHC. The work is focused on the GMSB scenario where a stau is the next-to-lightest SUSY particle (NLSP) and decays into a gravitino with lifetime cτNLSP in the range 0.5 m to 1 km. We study the identification of long-lived sleptons using the momentum and time of flight measurements in the muon chambers of the ATLAS experiment. A realistic evaluation of the statistical and systematic uncertainties on the measurement of the slepton mass and lifetime is performed, based on a detailed simulation of the detector response. Accessible range and precision on √F achievable with a counting method are assessed. Many features of our analysis can be extended to the study of different theoretical frameworks with similar signatures at the LHC.