Abstract:The non-periodic structure’s dispersion equation and the sound attenuation equation have been given based on the one-dimensional model of sound propagation. The relationship between the geometry parameters of drill strings with the dispersion characteristic as well as the attenuation characteristic is investigated numerically for a non-periodic drill string system, and the FEM software- ANSYS were used to confirm the theory results. The results shows that the dispersion characteristic of a non-periodic drill string system is identical with the result from of 'and' operation of dispersion characteristic of multiple periodic structure systems.The non-periodic structure’ passband is narrow while the stopband is wide, If the sound wave frequency were in the stopband, the acoustic attenuation would be larger than it in passband.