One means of tuning the symmetric poles or modes, without perturbing the counter-rotating family of poles or modes, of a planar disk resonator with top and bottom electric walls and a magnetic sidewall is to introduce a dielectric plug on its axis. The purpose of this paper is to investigate some intersections between the family of symmetric modes and that of pairs of degenerate counter-rotating modes in such a resonator using a commercial FE solver. The relative dielectric constant of the outer region of the resonator has been restricted to 14.1 while that of the inner region has been allowed to vary between 25 and 500. The paper includes three typical mode charts on this type of resonator as well as some standing wave solutions using an FE solver. The work has application in the design of triple pole circulators and filters. V V C 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE 17: 320-325, 2007.