An exact analysis of the modes Ⅱ and Ⅲ problems of a penny-shaped crack in a transversely isotropic piezoelectric medium is performed in thispaper.The potential theory method is employed based on the general solution ofthree-dimensional piezoelasticity and the four harmonics involved are represented byone complex potential.Previous results in potential theory are then utilized to obtainthe exact solution that is expressed in terms of elementary functions.Comparisonis made between the current results with those published and good agreement isobtained.