This paper is concerned with structural health monitoring techniques for pipe wall thinning using ultrasonic guided wave methods. First, our inspection model can be represented by linear elastic systems on a cylindrical shell. Secondly, numerical scheme of inspection is developed by Fourier-Galerkin approximations. Thirdly, we propose a computational method for identifying position, range, and sizing of flow accelerated corrosion (FAC). Finally, the effectiveness and validity are demonstrated through computational experiments.