© 2017, Springer-Verlag Berlin Heidelberg. This work addresses the evaluation of the displacement field in an elastic matrix due to the presence of an embedded homogeneous inclusion under time-harmonic SH-wave loads. We consider the bond between the circular cylindrical inclusion and the surrounding matrix of infinite extent to be partly damaged in the circumferential direction. The material of both inclusion and matrix is modelled as homogeneous, isotropic, and linearly elastic. An analytical approach is introduced here for describing the scattering of SH-waves by inclusions with partly damaged bond. Subsequently, a numerical example serves to illustrate the methodology, which can be extended to the scattering of SV/P-waves in a straightforward manner.