Green's function analysis of an ideal hard surface rectangular waveguide is proposed for characterization of the modal spectrum of the structure. A decomposition of the hard surface waveguide into perfect electric conductor and perfect magnetic conductor waveguides allows the representation of dyadic Green's function as a superposition of transverse magnetic (TM) and transverse electric (TE) waveguide modes, respectively. In addition, a term corresponding to a transverse electromagnetic (TEM) mode is included in the eigenmode expansion of the Green's dyadic. It is shown that the TEM mode solution can be obtained by solving vector Helmholtz's equation in the zero cutoff limit with the corresponding boundary conditions of electric field on the ideal hard surface. The electric field distribution due to an arbitrarily oriented electric dipole source is illustrated for a few representative TM, TE, and TEM modes propagating in the ideal hard surface rectangular waveguide. The proposed model is verified by analyzing a realistic hard surface square waveguide using the Ansoft High-Frequency Structure Simulator (HFSS).