We studied the spectroscopic properties of two thulium-doped Lu3Al5O12 (Tm:LuAG) samples with Tm3+ concentrations of 0.5 and 5 at.%. Judd-Ofelt theory was used to analyse the absorption spectra and to determine the radiative transition rates. Fluorescence measurements were further performed to determine the luminescence quantum efficiencies. The average radiative lifetimes of the H-3(4) and F-3(4) levels were calculated to be 1041 +/- 143 mu s and 17.7 +/- 3.4 ms, respectively. We observed a sharp increase in the strength of cross relaxation for the 5% Tm:LuAG sample evidenced by the much shorter fluorescence lifetime of 42.3 mu s for the H-3(4) level, in comparison with 851 mu s for the 0.5% Tm:LuAG sample. This was further supported by the relative emission measurements at 1470 and 1800 nm. The measured fluorescence lifetime of the 3F4 level showed a smaller decrease from 11.2 ms (0.5% doping) to 7.1 ms (5% doping). By using the Judd-Ofelt theory, the stimulated emission cross section was further calculated to be 1.2 +/- 0.2 x 10(-21) cm(2) at 2023 nm, corresponding to the free running wavelength of Tm:LuAG lasers. Finally, the critical distance parameter R-0 for cross relaxation was determined to be 10.2 +/- 0.8 angstrom from the fluorescence decay data.