This work presents the use of an explicit-form Green’s function for 3D general anisotropy in conjunction with the dual reciprocity boundary element method and the radial integration method to analyse elastodynamic problems using BEM. The latter two schemes are to treat the inertial loads in the time-domain formulation of the dynamic problem. The direct analysis with the Houbolt’s algorithm is used to perform the transient analysis. The efficient and accurate computation of the fundamental solutions has been a subject of great interest for 3D general anisotropic materials due to their mathematical complexity. A recently proposed scheme based on double Fourier series representation of these solutions is used to this end. Numerical examples are presented to demonstrate the feasibility and successful implementation of applying these schemes in synthesis to treat 3D elastodynamic problems of anisotropic materials.