The solution of the diffraction of sound waves by an axially moving fluid cylinder is obtained. Results indicate that there is no Doppler frequency shift for the scattered wave and when the angle of incidence is normal to the cylinder axis, the scattered wave is independent of the movement of the medium. Numerical computations for the magnitudes as well as the radiation patterns of the scattered wave as a function of the velocity of the moving medium were also carried out for various incident angles. It is found that the magnitudes and the radiation patterns of the scattered wave are quite sensitive to the variation in the angle of incidence even for slow relative movement of the fluid media.