This paper describes the study of the acoustic field of a fluid-filled pipe subjected to axial stress based on the acoustoelastic theory. The pipe with applied axial stresses can be approximated as a transversely isotropic pipe, and hence, its acoustic fields can be expressed using potential functions. The velocity changes of longitudinal wave modes with applied stresses are analyzed for the pipe filled with oil by an analytical method. It was found that the longitudinal mode velocity changes almost uniformly with the applied stresses. The high speed and low frequency plateaus of longitudinal wave modes are sensitive to stress. The relationship between stress and the velocity change of the guided wave is given. The results indicate that non-destructive testing techniques using longitudinal wave modes have strong potential to identify and monitor the stress levels in pipe structures.