Solutions of the wave equation are obtained for TE0mnand TMlm0modes in cylindrical cavities containing a coaxial, annular plasma column. The radial electron density distribution is assumed to be of the formne=n0[1−&ggr;1(r/a)2−&ggr;2(a/r)2], wheren0, &ggr;1, and &ggr;2are constants andais the outer radius of the plasma. The results can be used to determine the effects of density gradients on measurements of electron densities and collision frequencies by the cavity method. Some illustrative examples are presented.