This paper presents a signal processing technique for guided ultrasonic waves in a singlelayer hollow steel cylinder. The semi-analytical finite element (SAFE) method is used to compute dispersion curves for axisymmetric modes. Three-dimensional finite element modeling of L(0,1) and T(0,1) guided modes in a steel pipe with an internal defect is performed. The 2D fast Fourier transform is used for post-processing of the displacement field predicted by FE modeling in order to compute the power coefficients of the reflected and transmitted guided modes by the hidden defect. Energy conservation is demonstrated with errors below 1% across all defect depth ratios. The numerical findings are validated against established results from the published literature. Based on sensitivity, dispersion characteristics, and signal clarity, T(0,1) emerges as the most suitable mode for practical inspection of hidden defects in steel tubular structures.