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A method is presented for filtering dilute red blood cell suspensions through polycarbonate filters which avoids buildup of deposits on the pores and allows the determination of relative resistance of flow, with and without cells. In the small size range (pores 2.6–3 μm), the relative resistance falls from a high value at low ΔPs to an asymptotic value that depends on hematocrit at high ΔP. Using a model for cell flow in the pores, an estimate for the apparent membrane viscosity is attained which is a function of shear rate. The large pore sieves (4.15–5 μm) displayed little sensitivity of relative resistance to imposed ΔP. The possible importance of the results for understanding precapillary sphincter control of red blood cell distribution in capillary beds is discussed.