The three-dimensional problem of the effect of a rigid circular inclusion on the bending of a thick elastic plate is solved approximately by the method of E. Reissner (1, 2). Comparison is made for the limiting cases of vanishing inclusion size, (plane strain), and vanishing thickness (Poisson-Kirchoff plate theory), with the work of J. N. Goodier (3) and M. Goland (4). Graphs showing the transition from the plane-strain solution to the Poisson-Kirchoff solution are given. Stress concentrations are calculated and plotted versus the inclusion diameter-plate thickness ratio. The stress concentrations are found to be less than predicted by the classical plate theory when the inclusion diameter approaches the same order of magnitude as the plate thickness.