Abstract: The semi-analytical solution of scattering of plane SH waves by underground inclusion with arbitrary cross-section in half-space is presented using wave functions expansion method combined with boundary discrete method. Monte Carlo method is used to randomly generate 30 samples for cross-section shape of the inclusion, and the effect of cross-section-shape randomness on scattering of plane SH waves are studied by statistical analysis of the surface displacement amplitudes. It is shown that, cross-section-shape randomness has significant effect on the scattering of SH waves around an inclusion in half-space. When the variation coefficient of inclusion radius is equal to 0.1, for an inclusion of circular shape, the variation coefficient of surface displacement amplitude may be up to 0.71. The variation coefficient increases as the incident frequency increases. The variation coefficient increases as the inclusion rigidity decreases. The variation coefficient decreases as the inclusion depth increases.