A new elegant, powerful and accurate superposition method is presented for isotropic/specially orthotropic rectangular plates with arbitrary transverse load and arbitrary combination of free/simply-supported/clamped/guided/elastically supported edges. All the component solutions used here are infinite series equivalents of the complicated closed-form Levy-type solutions employed in the conventional superposition method; it is shown that these series equivalents are easily derived. The mathematical equations pertaining to the various component solutions required for the application of this new method to any plate problem are clearly presented. A number of validation studies are carried out to verify the accuracy of the method. The method can be directly extended to the analysis of more complicated plates made of multifunctional or functionally graded materials. © 2007 Elsevier Ltd. All rights reserved.