A new method of fundamental solution based on complete spherical wave potential (SWP-MFS) is proposed to solve 3-D elastic-wave scattering and dynamic stress concentration. The method established the boundary integral equation according to the boundary condition. The solution was solved by placing the spherical wave sources of compressional wave and shear wave on a virtual boundary based on the single layer potential theory. Through comparing with other available results

the excellent numerical accuracy and stability of the SWP-MFS are validated. The method was demonstrated in an example of the 3-D scattering of P or SV waves around an inclusion and a cavity in elastic full-space. Several important conclusions about scattering of 3-D elastic waves around an inclusion were obtained. As the modulus ratio decreases (the inclusion becomes softer)

the displacement amplitude spectrums oscillate more rapidly with large amplitude. For horizontal incident P waves

it seems that the dynamic stress concentration effect is more pronounced near the top and bottom of the spherical cavity

while it is more obvious near the two 45-degree angles of the longitudinal section for horizontal incident SV waves. Compared with employing the Green’s functions of concentrated force

the fundamental solution of SWP-MFS is more concise and easy to use

and provides a new meshless boundary-type method for elastic waves analysis.