In　order　to　inspect　longitudinal　stress-corrosion　cracks　of　large-diameter　functionally　graded　pipes　more　efficiently,　guided　circumferential　waves　in　infinitely　long　hollow　cylinders　were　studied　by　an　orthogonal　polynomial　approach.　Properties　of　material　were　assumed　to　vary　in　the　direction　of　the　thickness　according　to　a　known　radial　variation　law.　The　formulation　was　based　on　linear　three-dimensional　elasticity.　Results　from　homogeneous　cylinders　were　compared　with　that　published　earlier　to　check　up　the　accuracy　and　range　of　applicability　of　the　proposed　approach.　The　guided　circumferential　wave　dispersion　curves　of　graded　pipes　under　different　gradient　functions　were　calculated,　and　the　effect　of　the　gradient　functions　on　dispersion　curves　was　shown.　Finally,　the　guided　circumferential　wave　dispersion　curves　of　graded　pipes　under　different　ratios　of　the　inner　radius　to　thickness　were　calculated　to　observe　the　effect　when　the　ratio　varied　on　the　dispersion　curves.