ABSTRACT We calculate the complex dielectric constant of brine saturated sedimentary rocks using several different models. A calculation using a self-consistent scheme gives Archie’s law in the d.c. limit. The cementation exponent, m, is shown to depend on grain shape, in agreement with experiments. The theory also agrees well with dielectric constant and conductivity measured at 1.1 GHz on fused glass heads. It is shown that by including special geometrical features, such as high aspect ratio particles, the experimentally observed salinity and frequency dependence and the extremely high values of dielectric constant at low frequencies can be explained. Rigorous bounds on the dielectric and conductivity values of a rock composite also show that large values of dielectric are possible. The polarization of the ions at the rock-water interface equally give rise to high values of dielectric constant.