Abstract: The steady-state scattering of compressional wave (P-wave) by an absorbing cylinde ris investigated.The simple expressions for the scattered field caused by a normally incident plane P-wave are derived.The scattering cross sections for both non-absorbing and absorbing cylinders are calculated.Results show that for high velocity cylinder scatterer,the curves of scattering cross sections are smooth and oscillatory with ka,and the calculating scattering cross sections for non-absorbing and absorbing cylinders exhibit similar behavior.For low velocity cylinder scatterer,it can be seen from the scattering cross sections that a number of narrow peaks superimpose on a smooth background.The more the difference in corresponding velocity in the two media is,the more the peaks are,the nearer the values of maximum and minimumare,the denser the narrow peaks are,and the peaks will be decreased by the absorbing effects of cylinder.The scattering cross sections are small irregular oscillation while the corresponding velocity difference between the scattering cylinder and the matrix media is very small.