To explain the shear-thinning behavior of untreated carbon nanotube (CNT) suspensions in a Newtonian matrix, a new set of rheological equations is developed. The CNTs are modeled as rigid rods dispersed in a Newtonian matrix and the evolution of the system is controlled by hydrodynamic and rod-rod interactions. The particle-particle interactions is modeled by a nonlinear lubrication force, function of the relative velocity at the contact point, and weighted by the contact probability. The stress tensor is calculated from the known fourth-order orientation tensor and a new fourth-order interaction tensor. The Fokker-Planck equation is numerically solved for steady simple shear flows using a finite volume method. The model predictions show a good agreement with the steady shear data of CNTs dispersed in a Newtonian epoxy matrix as well as for suspensions of glass fibers in polybutene,(1) demonstrating its ability to describe the behavior of micro- and nanoscale particle suspensions. (c) 2013 American Institute of Chemical Engineers AIChE J, 60: 1476-1487, 2014