Several catalogs giving results of circular plates with a central hole with various loading and edge conditions have been published. However, these do not cover the case where each edge is supported, either simply or clamped. The usual recommendation is to solve these cases by superposition from the known elementary cases. This is not easily done. The results of the following two cases are given in this paper: (a) Inner and outer edge clamped; (b) inner and outer edge simply supported.