Abstract: A cross-flow filtration device which receives a feed stock at a feed end face and separates the feed stock into filtrate and retentate. The device has a structure formed from a plurality of substantially parallel monolith segments of porous material, each segment having a plurality of passageways which extend longitudinally from the feed end face to a retentate end face of the structure. The structure contains a filtrate conduit network comprised of both an intersegment filtrate conduit, formed by the arrangement of the segments, and at least one intrasegment filtrate conduit formed within at least one segment. The filtrate conduit network provides low pressure drop flow paths for filtrate flow through the porous material from the passageways to nearby filtrate conduits, and at least some of the passageways are separated from filtrate conduits by intervening passageways, thereby enabling a high ratio of passageway surface area to volume of the device and a high rate of filtrate removal.