We present a study of the thermodynamic and physical properties of Tl(5)Te(3), BiTl(9)Te(6), and SbTl(9)Te(6) compounds by means of density functional theory based calculations. The optimized lattice constants of the compounds are in good agreement with the experimental data. The electronic density of states and band structures are calculated to understand the bonding mechanism in the three compounds. The indirect band gaps of BiTl(9)Te(6) and SbTl(9)Te(6) compounds are found to be equal to 0.256 and 0.374 eV, respectively. The spin-orbit coupling has important effects on the electronic structure of the two semiconducting compounds and should therefore be included for a good numerical description of these materials. The elastic constants of the three compounds have been calculated, and the bulk modulus, shear modulus, and Young's modulus have been determined. The change from ductile to brittle behavior after Sb or Bi alloying is related to the change of the electronic properties. Finally, the Debye temperature and longitudinal, transverse, and average sound velocities have been obtained.