Analytical techniques are used to find the permeability of a model of a fibrous porous medium. The model is an array of thin annular disks periodically spaced in planes normal to the flow, where the repeating unit is a square or an equilateral triangle, and the planes are uniformly spaced in the flow direction. The solution of the Stokes equations for flow through the array is found by the method of distributed singularities, and the drag on a disk is estimated by an asymptotic technique in which the ratio of the radii of each annulus tends to unity. From the drag, the flow resistance or permeability of the array is found. By matching the thin disks to thin rings (tori), the array simulates fibrous materials like filters, in which the fibers are curved, perpendicular to the flow, and randomly oriented. Calculations of permeability are made for various ring sizes and spacings, for three array configurations, and for solid volume fractions in the range 0.0002-0.02. The results show that minimum permeability generally occurs for the most uniform distribution of solid material in a plane. Comparisons with equivalent rod arrays reveal that ring arrays generally have higher permeabilities, even though the rings create more tortuous flow paths.