Abstract: In order to inspect longitudinal cracks of anisotropic pipes more efficiently, guided circumterential waves in infinitely long orthotropic hollow cylinders are studied by an orthogonal polynomial approach. The formulation is based on linear three-dimensional elasticity. Results are compared with the finite element simulation to check up the accuracy and range of applicability of this polynomial approach. The group velocity dispersion curves and displacements distributions of guided circumferential waves for orthotropic cylindrical curved plate are calculated and appropriate frequency and modes that can be used to detect a longitudinal defect are found. Finally, finite element methods are used to simulate the detection and location of a longitudinal defect.