A micromechanical model for the flow of in-plane randomly oriented concentrated fiber suspensions in molten polypropylene has been combined with the Rutgers-Delaware model for Herschel-Bulkley materials. At high fiber volume fractions, Coulombic friction forces and hydrodynamic lubrication forces generated at the contact points between fibers are the dominant fiber-fiber interaction mechanisms. This feature has been shown here in both steady-state and oscillatory shear. The complex viscosity and the steady-state viscosity of the suspensions were measured as a function of an effective strain rate, which was defined as the strain rate in steady-state shear and the product of the strain and the frequency in oscillatory shear. Four distinct strain regions were identified: viscoelastic behavior below an apparent yield stress, pseudosolid plasticity at low effective sheer rates above the yield stress, a viscous Newtonian plateau at medium effective shear rates, and a shear thinning region at high rates. The two latter regions were related to the viscosity-shear rate curves of the neat resins. The testing method, new for such fiber suspensions, allowed simple and rapid access to the shear parameters of the materials. Effects of mat structure, resin viscosity, and differences between different materials may be obtained.