Analytical expressions for the deflection surface of symmetrically loaded circular and annular plates resting on discrete point supports are derived. The formulation of the problem is based on classical small deflection plate theory. It is also assumed, in the formulation, that the supports are situated equal distances apart on a single concentric circle. There is no restriction placed on the number of supports or on the size of the support circle which could be as large as the plate itself or as small as the size of the hole of the annular plate. The singularity effects associated with the concentrated supports on the plate problems considered here are accounted for in the solution, by drawing an analogy from the Michell's solution to a clamped circular plate subjected to an eccentric point load. This procedure yields solutions in much more suitable form for practical numerical problems than other known methods. In the case of circular plates on multipoint supports, explicit solutions are given to a number of loading conditions. Solutions to a uniformly loaded circular plate on multipoint supports are compared with the published experimental results; the conclusions are favorable. From the numerical data obtained for a uniformly loaded circular plate on multipoint supports, a procedure is outlined for obtaining contour maps of deformed uniformly loaded plates with discrete supports on two support circles. Solutions to annular plates on multipoint supports are derived for the first time. By utilizing this result, design charts are drawn to indicate the optimum size of the support circle, which would produce least peak-to-peak displacements for any given size of hole, and a specified number of supports. Contour maps associated with annular plates on three point supports are also drawn to illustrate the influence of support circle on the displacements. It was found that when there are a fewer number of supports and/or the size of the hole is small, the magnitude of peak-to-peak displacements and the size of the optimum support circle are considerably different from the associated quantities when the support is a continuous ring. / Ph. D.