Few studies have been reported to investigate the wave fields in a layered wedge-shaped space.The indirect boundary element method was used to solve the wave fields in a layered wedge-shaped space for incident plane SH-waves.Firstly

the layered wedge-shaped space was extended to the layered half-space and the free are fields corresponding to the layered half-space for incident plane SH-waves were calculated.Secondly

virtual uniformly distributed loads were applied on the slant edge of the layered wedge-shaped space to simulate the influence of the slant edge on the wave fields

and the densities of the virtual uniformly distributed loads can be obtained by the corresponding boundary conditions.Finally

the free wave fields of the layered halfspace are added to the wave fields induced by the uniformly distributed slant edge load to obtain the total wave fields.The method was verified and numerical calculation and analysis were performed.The numerical results show that the wave field in a layered wedge-shaped space is obviously different to that in a uniform wedge-shaped space

and the presence of the layer makes the surface displacement amplitudes very complex depending on the incident angle.And the study will lay a foundation for future works of solving the wave fields in a layered wedge-shaped space for incident P

SV and Rayleigh waves.