- A finite element formulation for the bending of thin and thick plates based on least-squares variational principles is presented. Finite element models for both the classical plate theory and the first-order shear deformation plate theory (also known as the Kirchhoff and Mindlin plate theories, respectively) are considered. High-order nodal expansions are used to construct the discrete finite element model based on the least-squares formulation. Exponentially fast decay of the least-squares functional, which is constructed using the L2 norms of the equations residuals, is verified for increasing order of the nodal expansions. Numerical examples for the bending of circular, rectangular and skew plates with various boundary conditions and plate thickness are presented to demonstrate the predictive capability and robustness of the new plate bending elements. Plate bending elements based on this formulation are shown to be insensitive to both shear-locking and geometric distortions. 2004 John Wiley and Sons, Ltd.