Abstract This paper presents an accurate semi-analytical technique to analyse piezoelectric plates. The proposed technique is built upon the scaled boundary finite-element method. No kinematic and electrostatic assumptions are introduced in the derivation process. The in-plane dimensions are divided into 2D elements and the 3D geometry is obtained by translating the mesh in thickness direction. The through-thickness solutions are expressed analytically with a matrix exponential function. The 3D-onistent nature allows the proposed technique to describe the through-thickness behaviour of piezoelectric plates accurately. Numerical shear locking does not arise. Four numerical examples are presented to highlight the performance of the proposed technique.