The problem of bending of thin elastic plates has interested mathematicians and engineers for many years. Various methods have been put forward for determining the approximate solutions among which the variational method of Ritz is most common. This procedure leads to a system of linear simultaneous equations, the solution of which is often quite tedious, although generally by taking a few rows and columns quite accurate results are obtained. The purpose of this note is to show that by using bar eigen-functions for plates which are either clamped, or when some edges are freely supported, certain simplifications can be made in the process and the difficulty of solving simultaneous equations can be avoided; and that the deflection surface of the plate can be derived directly in a series form.