Two general solutions for a circular flat plate with or without a central hole subjected to uniform annular line loads, either transverse force or bending moment, are presented in this paper. Coefficients for use in formulae derived are presented in both mathematical and graphical forms so the formulae can be used conveniently to analyze a range of different circular plates. Several examples are used to demonstrate the application of the formulae and the results received are compared with results from a finite element analysis.