Abstract: To address the structural health monitoring for a crack originating from a fastener hole in aerospace aluminum alloy structures, this study investigates the incremental scattering of out-of-plane displacements induced by hole-edge crack for the Lamb wave S₀ mode, considering the influence of the initial structural features of the fastener hole on the baseline signals in active Lamb wave monitoring. Starting from the fundamental governing equations for isotropic plate, the displacement field is expanded using Legendre orthogonal polynomials, and material parameters are treated as spatially varying functions. Based on these formulations, the characteristic equations for Lamb wave mode coupling in isotropic elastic plate are derived, which systematically reveals the coupling mechanism between out-of-plane and in-plane displacements of the S₀ and A₀ modes. A linear three-dimensional finite element model is then established to simulate the interaction between ultrasonic Lamb waves and hole-notch defects. A hybrid compensation algorithm that accounts for both dispersion and geometric spreading losses is developed, along with a circumferential incremental scattering coefficient calculation method based on baseline subtraction. A scanning laser Doppler vibrometry system is constructed to experimentally characterize the far-field out-of-plane scattering of the S₀ mode under various excitation frequencies and incident angles. Numerical and experimental results consistently demonstrate that hole-edge cracks significantly affect the amplitude and directivity of the incremental scattering of the S₀ mode, with increased sensitivity observed when wave propagation is aligned parallel to the crack. Furthermore, the study elucidates the backscattering mechanism of Lamb waves caused by hole-edge cracks.