Directional permeability membranes were designed, fabricated, and tested with the potential application of facilitating drug delivery. Membranes were constructed from two porous polyimide sheets with offset pores and bonded with double sided tape with thickness values of 20 or 70 μm at the perimeter. The pores ranged in diameter from 0.25 to 1.0 mm and were cut using a laser micromachining apparatus. The pores were arranged in a square array with distance of 2 mm from center to center. The membranes were tested under pressure-driven water flow in the range of 0.01–0.10 m of H2O and flow rates were measured for two configurations: one with the thicker sheet upstream (forward direction) and one with the thinner sheet upstream (reverse direction) and the ratio of forward/reverse flow was calculated. In order to better understand membrane behavior, the maximum deflection of the thinner sheet was measured using an imaging system composed of a lens with small depth of field, digital camera, motorized linear translation stage, and a motion controller. Results show that in forward flow, by increasing hydrostatic pressure from 0.01 to 0.10 m H2O the mass flow rate increased by 40–55%. Conversely, increasing the hydrostatic pressure in the reverse direction from 0.01 to 0.10 m H2O considerably reduces the flow rate. The ratio of forward to reverse flow rate of the membrane varied in the range of 1.5 to 9529, depending on the pressure head.