Abstract: This paper deals with crack problems in transversely isotropic piezoelectric material. The formulations of Bueckner work conjugate integrals in these kinds of materials are presented. Furthermore, by introducing two kinds of supplementary "stress-displacement and electricdisplacement-electric field potential" fields, it is proved that are simple but universal relationsbetween the Bueckner work conjugate integral and the J--integral and between the Bueckner workconjugate integral and the M-integral in these ...