To obtain anti-plane elastodynamic analytic solution of a semi-circular cylinder, subject to anti-plane point source loading in a vertical bound of an elastic quarter space, image method and wave function expansion method are employed to study steady state scattering of the semi-circular cylinder and interaction of bounds, then displacement and stress are determined in this quarter space. More specifically, firstly, the quarter space is extended as a half space, and the semi-circular cylinder is also extended as a circular cylinder. Then, displacement wave is constructed as series form of wave function and circular cylindrical bound is expanded as Fourier series to determine coefficients of wave function finally. Dynamic stress distributed around circular cylinder is calculated to show that scattering of the semi-circular cylinder is apparently to distinguish front and back, and relative low frequency of loading usually causes more dynamic stress around the semi-circular cylinder, and material parameters also have two widely divergent influences on the radial and circumferential dynamic stress distribution. This steady state solution is presented to enrich SH wave scattering theory and to formulate Green function method for SH wave scattering of bi-material interfacial circular cylinder with theoretical analysis. Numerical calculating examples demonstrate the related engineering problem for underground engineers, earthquake engineers, geotechnical engineers and civil engineers as well.