This paper deals with resonance effects in circularly cylindrical solid bodies of high‐&egr; dielectrics such as titanates, these bodies being either not metallized or partly or fully metallized by fired‐on silver. The high dielectric constant has two pronounced effects:(a) Miniaturization, a linear reduction in size in the order of magnitude of 1/100, and(b) Realization of boundary conditions approaching infinite wave impedance.All four combinations of radial and axial wave impedance being zero (metallized) or infinite (interface dielectric/air) are investigated mathematically and experimentally. Special consideration is given to degenerated modes; that is, modes for which the axial dimensions of the cavity do not contribute to the resonance wavelength. Because of the inherent magnetic leakage through the dielectric, this is only conditionally true. These modes are therefore termed quasi‐degenerated.In contrast to conventional cavity theory dealing only with metallic boundaries, quasi‐degeneratedTEmodes are realizable; namely, if the faces of the cylindrical cavities are not metallized. These cavities can be tuned by introducing magnetic rods into them or by application of conductive disks outside of them in the proper position.A novel type of antenna can be evolved from theTE010∞∞mode, comprising a dielectric spiral encircling a magnetic rod.In many cases the relatively high temperature coefficient, dissipation factor, and noise level prevent for the time being the potential application of these high‐&egr; dielectrics.