Both multi-layer piezoelectric cantilevers and multi-layer piezoelectric composite cantilevers are studied based on 2D linear theory of elasticity and piezoelectricity. Both the piezoelectric coefficient and the thickness for different layers are taken as variables. As opposed to traditional investigations based on the elementary theory of elasticity, the present investigation gives exact solutions for the variation of these parameters by introducing several recurrence formulae. The solutions obtained in the present paper are compared with numerical results and the results obtained by other investigators; good agreement is found. (Some figures in this article are in colour only in the electronic version)