Abstract: Ultrasonic guided waves have a good potential for application in non-destructive testing of typical defects in plates. Considering the uniqueness of the semi-infinite domain cladding structure, the shear horizontal (SH) guided waves propagate in the substratum with energy leakage, which leads to the attenuation characteristics of the SH guided waves. For the propagation characteristics of SH guided waves in cladding plate with semi-infinite domain, a theoretical solution based on the Legendre series expansion method is proposed in this study. The dispersion characteristic equation of SH guided waves is derived by the state vector method, and the matrix equation is constructed by the Legendre series expansion method, then the dispersion curves and attenuation curves of SH guided waves in semi-infinite domain cladding structures are solved synchronously by the form of eigenvalue solution. The results of the proposed method are compared and analyzed with those of Disperse software by taking the steel substratum semi-infinite domain cement cladding as an example, and both of them are in good agreement, which verifies the accuracy of the theoretical solution. In addition, the dispersion curves and attenuation curves are accurately obtained by analyzing and calculating different cladding materials and transverse isotropic material substratum, demonstrating the universality of the described algorithm. Finally, a finite element simulation model of the steel substratum cement cladding structure is established to explore the interaction between the SH guided waves and the bonding defects, and the quantitative characterization of the bonding defects is achieved through the attenuation coefficient.