Due to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou  are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.