The displacements and stresses for various thickness-to-span ratios were obtained using the boundary element method (BEM) for Reissner’s moderately thick plates, and the finite element method (FEM) for Mindlin’s moderately thick plates and three dimensional problems.The applicable range and accuracy among the three dimensional theories, the moderately thick plate theory and thin plate theory were defined. A theory basis and reference for choosing the thin plate theory, the thick plate theory or the three dimensional theory to analyze plates were provided. The results have shown that shear locking is deleted when the reduced integration is used in the finite element of plates and shells.