It is postulated that porous media is made up of fractal solid skeleton structure and fractal pore surface. The model thus developed satisfies measured anomalous dielectric behavior of three distinctly different porous media: kaolin, montmorillonite, and shaly sand rock. It is shown that the underlying mechanism behind dielectric dispersion in the kHz range to high MHz range is indeed Maxwell–Wagner mechanism but modified to take into account the multiphase nature of the porous media as opposed to the traditional two-phase Maxwell–Wagner charge accumulation effect. The conductivity of the surface water associated with the solid surface and charge accumulation across the surface irregularities, asperity, and bridging between particles at the micro-scale-level pores are shown to contribute to this modified Maxwell–Wagner mechanism. The latter is dominant at low frequencies. The surface water thickness is calculated to be about 2–6 nm for a variety of porous media. ©1997 American Institute of Physics.