In the present paper, two kinds of thick-walled hollow cylinders are studied. One is the cylinder with multi-layers and another is functionally graded cylinder. Both the cylinders are made of piezoelectric materials. Based on the basic piezoelectric equations, the exact solutions for the elastic hollow cylinder with N-layers submitted to external voltage are obtained. For the graded hollow cylinder the exact solutions are obtained by using displacement method and three hypergeometric functions. Comparisons demonstrate that the limitation of the multilayer cases is consistent with that of graded cases.