The methods of Green’s function, complex variable function and multi-polar coordinates are applied to report interaction of elliptical elastic inclusion and an arbitrary length of crack at any position under incident SH-waves. The "conformal mapping" technology was developed to solve SH-wave scattering displacement field and a Green’s function, the fundamental solution to the displacement field for elastic half space containing elliptical inclusion while bearing out-plane line source load at arbitrary point, which will be utilized to create a beeline crack with arbitrary length at any position based on “crack-division” technology. The displacement field and stress field of elastic half-space possessing elliptical elastic inclusion and a crack were then deduced. Numerical examples are presented to analyze the dependence of dynamic stress concentration factor (DSCF) around the elliptical inclusion, the horizontal surface displacement and dynamic stress intensity factor (DSIF) at crack tip on different parameters.