The paper presents a theoretical description of induced polarization decay in ion-conductive rocks, which develops the steady-state model of Friedrichsberg - Sidorova based on the diffusion nature of induced polarization. Grain contacts and pore space filled with interstitial liquid are regarded as narrowing and broadening current conduits that are characterized by different transport numbers. An analytical solution of the unsteady diffusion equation yielded an expression describing time constants of induced polarization for a model in which wide pores are much longer than the narrow ones. Experimental transient characteristics obtained for sands with different average grain sizes are consistent with the suggested theory. According to theoretical and experimental results, the time constant of induced polarization decay for pure sand is proportional to the square of its average grain size.