Abstract: The scattering of SH wave and the dynamic stress concentration by a moving rigid cylinder in an elastic half space are studied with complex functions and multi-polar coordinate method. The scattering wave which satisfies the condition of stress free on the ground surface of a half space containing a moving rigid cylinder impacted by incident steady SH-wave is constructed by the base of the symmetry of SH-wave scattering and the method of multi-polar coordinate system. By taking the advantages of the boundary conditions around the moving rigid cylinder, the solution of the problem can be simplified as a series of algebraic equations which can be solved numerically by truncating the finite terms of the infinite algebraic equations. Thus expressions of displacement and stress are established while the moving rigid cylinder in the half space is in existent and the expression of dynamic stress concentration factors (DSCF) around the inclusion is given. Finally, the influencing factors to the problem are discussed through some actual examples.