A small concentration of thin plate‐like insulating material in a conducting host can give rise to anomalously high values of dielectric constant. For a small concentration &eegr; of oblate spheroidal grains (a ≪ b=c) with depolarization factor along symmetry (a) axisLs= 1−&dgr;,&dgr; = &pgr;a/2b, the static value of the dielectric constant of rock &egr;sand dc conductivity &sgr;(0) are given for (a) &dgr;<&eegr; as &sgr;(0) = &dgr;&sgr;R/&eegr;, &egr;s≅&egr;m/&eegr;, and for (b) &dgr;≳&eegr; as &sgr;(0)≅&sgr;R(1−&eegr;/&dgr;), &egr;s≅&eegr;&egr;m/&dgr;2. Case (a) corresponds to the well‐known Maxwell–Wagner effect with &egr;sdiverging as &eegr;→0, and &sgr;(0)→0. Case (b) gives a novel result that &egr;smay diverge for &dgr;≳&eegr;≫&dgr;2, with a nonvanishing &sgr;(0). Case (b) is applied to explain frequency and salinity dependences and the large values (∼103, observed at MHz frequencies) of the dielectric constant of conducting sedimentary rocks. Possible reasons for the larger values (∼106) observed experimentally at lower (khz) frequencies are discussed.