This work is a part of a project aiming at the construction of an implantable artificial kidney. The first step of blood filtration is the separation of blood cells from plasma in the glomerulus. The cells (RBCs, WBCs, platelets, etc.) go back into circulation and plasma is subjected to a number of other filtration steps. Since we intend to power the filtration using the energy of pulsating natural blood flow, the filtration membrane for the artificial kidney is restricted to working in the systolic to diastolic pressure range. Optimization of the geometry of filtration pores in the membrane is presented here with an additional condition of reducing the possibility of pore clogging. Different pore geometries are compared, and a design is suggested in which the pressure drop is minimized for a given flow rate of the filtrate.