The method of moments was employed, in conjunction with the equivalent-source technique and the modal expansion theory, to analyze multi-groove and multi-mode circular radiators. No restriction was imposed on the number, width and depth of grooves, so the theoretical method and the analytical formulation are applicable to the analysis and design of wide-ranging coaxial grooved radiators. The problem of radiation from a multi-groove and multi-mode circular radiator embedded in an infinite ground plane was solved first. Then, expressions representing the elevation-plane patterns of the radiator embedded in a finite ground plane was derived using Geometrical Theory of Diffraction(GTD). The expressions for the field pattern were obtained by superposing the infinite ground plane solutions, the first-order diffracted field solutions and the axial caustic solutions in their respective regions of validity. The calculation results are in agreement with experiment measurements.