The resistance to the blood cells at the entrance to capillaries and membrane pores contributes considerably to the peripheral resistance in the blood circulation. This paper proposes, for the first lime, a simplified mechanical model in an attempt to treat the axisymmetric motion of a cell sliding into a circular pore. In this model, the shape of the cell is taken as given according to the microvideograph and the cell membrane is assumed to slide over its surface. The lubrication theory is applied to the thin layers of plasma between the membrane and the pore wall, yielding the pressure and shear stress distributions over the membrane as well as the resultant drag exerted on the cell. Our computations have simulated the process of the cell entering the pore, which is in qualitative agreement with the microvideographic observations.