The spectral analysis of the structural waveguide leads to the dispersion relation, which shows the behavior of the different wave modes with frequency. It helps in ultrasonic-guided wave-based non-destructive inspection to choose an excitation frequency based on the choice of the excitation wave mode(s). The dispersion curves for a waveguide with simple defect-free geometry work well for their inspection. However, it’s important to note that the presence of defects within the structure can significantly affect the wave dispersion behavior used for diagnostics. Therefore, the use of the dispersion curves of the defect-free waveguide for the inspection of the defective ones can yield less accurate inspection results. This emphasizes the need to conduct the spectral analysis of the structural waveguide with defects and investigate the sensitivity of dispersion curves to various defect parameters such as shape, size, depth, and orientation. The dispersion curves can be obtained analytically or numerically, but they have inherent limitations. The analytical methods are limited to simple geometry; however, using the numerical methods for complex geometry will require a substantial computational cost. Therefore, this paper presents the spectral analysis of the three-dimensional structural waveguide with defects using the Semi-Analytical Finite Element Method, which uses the advantages of both analytical and numerical methods. We have performed the spectral analysis of the simple geometry without and with defects (such as cracks or delamination) of varying sizes. It is observed that the finite element discretization of the cross-section affects the number and accuracy of wave modes obtained in the dispersion curves. The validity of the SAFE framework has been initially established by comparing the dispersion curves obtained from our SAFE formulation with those generated by GUIGUW (Bocchini et al. 2011), an open-source dispersion computation software, for a defect-free structural waveguide. Subsequently, we applied our SAFE formulation to compute dispersion curves for waveguides with defects. As the defects reduce the structure’s stiffness, we observed a significant reduction in the cutoff frequencies of the higher-order wave modes in the dispersion curves for defective waveguides compared to the defect-free waveguide.