A, new displacement function is obtained for the analysis of the bending of plates using rectangular finite elements which satisfies the conditions of compatibility across element boundaries as well as throughout the elements. The improvement in accuracy and convergence-is studied by com-paring the results of some problems with those obtained by Zienkiewicz and Cheung using a different displacement function. Also, some results are compared with known exact solutions and with the results obtained by other methods. Finally, a displacement function is proposed for the analysis of the bending of plates bounded by coordinate lines in polar coordinates, using elements consisting of annularsectors.