Abstract: Based on the integral representation of Dirac-delta function and Cauchy's theory of residues, the Green's function for two-dimensional anisotropic elastic media with piezoelectric, piezomagnetic and magnetoelectric coupling effects is derived. The novel features of the present Green's function are summed up as: (1) its expression is given in closed form; (2) it is applicable to not only in-plane problems but also anti-plane problems and problems in which in-plane and anti-plane deformations are coupled; (3) it remains valid for the cases of the degenerated materials.