Two simple plate bending elements, based on Mindlin theory for analysis of both moderately thick and thin plates, are presented in this paper. These elements have either four nodes or eight nodes with 12 and 24 DOF, respectively. To illustrate the accuracy of these finite elements named as TURE12 and TURE24, several numerical examples of displacements and stresses for both thin and moderately thick plate bending problems are presented and discussed with a range of finite element meshes and thickness-to-plate length ratios. In addition, the bending and shearing behaviours of a Mindlin plate are analyzed with respect to shear locking. In order to test the shear locking, the results obtained from the Mindlin plate analysis using 4- or 8-noded elements with full, reduced, and selective reduced integration are compared with the exact classical thin plate solution. (C) 2004 Elsevier Ltd. All rights reserved.