The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.