In　ultrasonic　nondestructive　inspection　of　large-diameter　pipes,　longitudinal　cracks　can　be　detected　more　efficiently　by　using　guided　circumferential　waves.　Based　on　linear　three-dimensional　elasticity,　an　orthogonal　polynomial　approach　is　used　for　determining　the　guided　circumferential　waves　in　homogeneous　infinitely　long　orthotopic　hollow　cylinders.　Results　are　compared　with　those　published　earlier　to　check　up　the　accuracy　and　applicability　of　this　polynomial　approach.　Guided　circumferential　wave　dispersion　curves　for　unidirectional　composite　pipes　under　different　fiber　intensity　are　calculated,　and　the　effect　of　the　variety　of　the　fiber　intensity　on　dispersion　curves　is　shown.　Finally,　the　guided　circumferential　wave　dispersion　curves　for　orthotropic　pipes　under　different　ratios　of　outer　radius　to　thickness　are　calculated　and　the　inherited　influence　of　the　variety　of　ratio　on　the　dispersion　curves　is　discussed.