A long thick-walled hollow cylinder ofpiezothermoelastic materials was studied in this work. The gradient property of the piezoelectric parameter g31 was taken into account. The theory of elasticity was applied to obtain the exact solutions of the cylinder subjected simultaneously to thermal and electric loadings. As an application, these solutions have been successfully used to study the inverse problems of the material. For comparison, numerical results have been carried out for both graded and double-layered cylinders.