Abstract: The fracture behavior of four non-symmetric radial cracks originating from a circular hole in piezoelectric composite materials subjected to remotely uniform in-plane electric loading and anti-plane mechanical loading was studied in this paper. The problem was transformed using the complex variable method and a new mapping function into Cauchy integral equations. By solving the Cauchy integral equations, the analytical solutions of electric and elastic fields and field intensity factors near the crack tip were obtained under the electrically impermeable and permeable assumptions. Several known results were the special cases of the present results and new models used for simulating more practical defects in piezoelectric composite materials were derived as well, such as three radial cracks originating from a circular hole, semi-circular hole with an edge crack originating from a semi-infinite plane and a semi-infinite plane with an edge crack. A well agreement of the analytical solutions with the finite element results shows the accuracy and efficiency of the present method. Numerical examples are provided graphically to show the effects of the geometrical parameters on the field intensity factors.