In this work, the rheo-optical response of multiwalled carbon nanotube (MWCNT) suspensions was analyzed. Dichroism was obtained using a polarization-modulation technique in parallel disks and for the first time for these particles in a Couette flow geometry. MWCNTs were dispersed in a Newtonian epoxy matrix, at different concentrations covering the dilute and semidilute regimes. Measurements of dichroism were performed as functions of shear rate and nanotube concentration. Surprisingly, the ultimate average orientation angle with respect to the flow direction was far from zero degree, even at high Peclet (Pe) numbers in very dilute suspensions. To explain this peculiar behavior, a new model for flexible rods, valid in the dilute regime, is proposed. It is based on the development of Strautins and Latz [Rheol. Acta 46, 1057–1064 (2007)] that considers flexible rods made of beads and connectors. We modified their bending potential that allows only straight rods at equilibrium with a harmonic cosine expression. This simple modification changes drastically the behavior of these flexible particles that exhibit a non-negligible orientation in the vorticity direction under steady state.