A theory was developed to describe the equilibrium partitioning of a flexible polymeric solute between a dilute solution and a medium consisting of a randomly oriented array of fibers (e.g., a fibrous membrane or gel). The fibers were regarded as long, rigid cylinders, and the solute was modeled as a chain consisting of n mass points joined by n - 1 rectilinear segments. Results were obtained for freely jointed chains and for chains with fixed bond angles, using a combination of analytical and computational (e.g., Monte Carlo) techniques. The predicted partition coefficient (Phi, the solute concentration in the fibrous material divided by that in the bulk solution) proved to be sensitive to the number of fibers included; typically, 50 or more nearest neighboring fibers were needed to obtain a convergent result. The values of Phi, decreased as fiber volume fraction, molecular size, or number of mass points was increased selectively. As the bond angle was increased from 0 degrees (a chain folding back on itself) to 180 degrees (a rodlike chain), Phi first decreased and then increased. The model predictions agreed reasonably well with literature partitioning data for various polymeric solutes in hydrogels, especially when the radius of gyration was no more than a few times the fiber radius. With the radius of gyration specified, the model predictions were fairly insensitive to whether the bond angle was fixed or random.