This paper presents an analytic solution for the diffraction of plane P waves by a cylindrical inclusion in half space by Fourier-Bessel wave function expansion method, in which the flat surface of half space is approximated by a large curved surface. The equation can be constructed by the continue boundary and the free surface condition. Based on parametric analysis, the impact of the inclusion on surface displacement amplitude is discussed. It is illustrated that there is large difference of the diffraction characteristics between the hard inclusion and soft inclusion. The displacement response depends strongly on the incident angle and frequency. The diffraction effect can be ignored with large embedded depth of the inclusion.