Both theoretical and numerical electromagnetic analyses about the modes inside the cylindrical cavity of superconducting electron cyclotron resonance ion source (SERSE) have been performed. Modes close to 14, 18 and 28 GHz frequencies, usually employed in SERSE operating conditions, have been calculated in vacuum and when the chamber is filled with a uniform non-collisional plasma at different electron densities. To consider the holes present in the chamber flanges, a numerical approach has been used, by means of the HFSS TM electromagnetic simulator, for the first mode in the cavity. Modes in a plasma-filled cylindrical cavity with holed bases have full width half maximum bandwidths larger with regard to the closed cavity in vacuum, and it leads to an increased mode frequency overlap. A monochromatic electromagnetic wave feeding this cavity can, in principle, excite different modes. Further investigations about the coupling between the SERSE cavity and its feeding waveguides have to be performed.