Multimode characteristics of a dielectrically loaded rectangular cavity are analyzed by a graphical method. Coupled transcendental equations for multimode frequencies may be solved graphlially. This shows that the resonant frequencies of the partially flued cavity with a dielectic are shifted toward lower frequencies compared to those of the empty cavity. It is shown that a perturbational scheme can not be employed to calculate multimode frequencies because of relatively large frequency shrift. Existence of the surface wave modes In the dielectric and their resonant frequencies are early predicted from this graphical method.