A model is proposed to describe the rheology of planar randomly oriented concentrated fiber bundle suspensions in a shear-thinning matrix. The approach is that, at high fiber volume fractions, the dominant interaction mechanisms are friction and lubrication at the fiber-fiber contact points. A fiber pull-out technique is used to measure the force per unit length exerted on a single fiber tow of elliptical, cross section embedded in a bulk suspension. By varying the tow velocity, fiber volume fraction, resin viscosity, and suspension structure, the factors affecting the lubrication and frictional components of the interaction forces were analyzed. The lubrication force is related to the flow behavior of the neat resin. The theoretical equations derived in this work allow for the computation of a shear viscosity of the suspension, which is in good agreement with experimental evidence. It is shown that dispersed fiber and dispersed fiber bundle suspensions are yield stress fluids.