Theoretical new equations for evaluating the hydraulic conductivity of compacted bentonites and bentonite-sand mixtures are derived for designing bentonite based buffer and backfill materials to fill high-level nuclear waste repositories. New equations for evaluating the velocity of interlayer-water flow between two montmorillonite layers considering the swelling behaviors of montmorillonite are proposed. Furthermore, a calculating method for the hydraulic conductivity of compacted bentonite and bentonite-sand mixtures is presented by combining the new equations with the equations for evaluating swelling behavior of montmorillonite in bentonite, which have already been proposed by the author. The applicability of this method was investigated by comparing the calculated results with laboratory test results on the hydraulic conductivity of compacted bentonites and bentonite-sand mixtures.