This paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method. The formulation is based on the three-dimensional governing equation without enforcing the kinematics of plate theory. Only the in-plane dimensions are discretised into finite elements. Any two-dimensional displacement-based elements can be employed. The solution along the thickness is expressed analytically by using a matrix function. The proposed technique is consistent with the three-dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon. Moreover, the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence. Numerical examples of various plate structures with different thickness-to-length ratios demonstrate the applicability and accuracy of the proposed technique. Copyright © 2012 John Wiley & Sons, Ltd.