Based on the complex poeential method, the Green's functions of tire phme problem hr transrerse O, isotropic piezoelectric media with an elliptic hole are obtahred in terms of exact electric boundaw conditions at the rhn of the hole. When the elliptic hole degenerates huo a crack, the fundamental sohttions for the field intensity factor's are given. The general sohttions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of the fundamental solutions. With the aid of these solutions, some erroneous results provided previously in other works are pointed out. More important is that these sohttions can be used as the f, mdamental solutions of boundat T element method to solve more practical problems h7 piezoelectric media.