We have fabricated paper- and nitrocellulose-based lateral-flow devices that are shaped in two dimensions by a computer-controlled knife. The resulting star, candelabra, and other structures are spotted with multiple bioassay reagents to produce multiplex lateral-flow assays. We have also fabricated laminar composites in which porous nitrocellulose media are sandwiched between vinyl and polyester plastic films. This minimizes evaporation, protects assay surfaces from contamination and dehydration, and eliminates the need for the conventional hard plastic cassette holders that are typically used to package commercial lateral-flow diagnostic strips. The reported fabrication method is novel, low-cost, and well-suited to (i) fabrication and adoption in resource-poor areas, (ii) prototype development, (iii) high-volume manufacturing, and (iii) improving rates of operator error.