Abstract: 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.