A study of high energy muons traversing the ATLAS hadron Tile calorimeter in the barrel region in the energy range between 10 and 300 GeV is presented. Both test beam experimental data and Monte Carlo simulations are given and show good agreement. The Tile calorimeter capability of detecting isolated muons over the above energy range is demonstrated. A signal to background ratio of about 10 is expected for the nominal LHC luminosity (1034 1/cm2s). The photoelectron statistics effect in the muon shape response is shown. The e/mip ratio is found to be 0.81 ± 0.03; the e/μ ratio is in the range 0.91-0.97. The energy loss of a muon in the calorimeter, dominated by the energy lost in the absorber, can be correlated to the energy loss in the active material. This correlation allows one to correct on an event by event basis the muon energy loss in the calorimeter and therefore reduce the low energy tails in the muon momentum distribution.