AbstractEquations of motion characterizing the flow of incompressible, time‐independent non‐Newtonian fluids, exhibiting the anomalous surface effect, through compressible porous media are developed. Approximations are made to arrive at workable filtration equations for slurries of non‐Newtonian (power‐law) fluids. The constant‐pressure and constant‐rate filtration relationships developed are verified experimentally using slurries of calcium carbonate in water and dilute CMC solutions. The anomalous surface effect is found to exist in the filtration of the non‐Newtonian fluids. The specific cake resistance in the case of the non‐Newtonian sludge and the ratio of the effective slip velocity to the pore velocity are found to be functions of both the CMC concentration and the pressure drop across the filter bed.