Impressive enhancements of the storage modulus have been documented when low volume fractions of single wall carbon nanotubes (SWNTs) are added to a Newtonian solvent for obtaining dilute suspensions. The intrinsic bending dynamics of carbon nanotubes (CNTs) has been proposed to explain such elasticity. CNTs contain topological defects inducing naturally bent structures in absence of external forces and, hence, a semiflexible filament with a bent configuration at minimal internal-bending-energy is used for mimicking the structure of SWNTs in suspension. Previous continuous model is discretized as a nonfreely jointed bead-rod chain with a naturally bent configuration for simulating the rheological behavior after a shear-strain step in linear regime of SWNT dilute suspensions by using a Brownian dynamics (BD) approach. In general, bead-rod chains exhibit an instantaneous relaxation after a high shear-strain step. Bending rigidity and number of constitutive rods are found to be determinant parameters in the internal-energy relaxation behavior of nonfreely jointed bead-rod chains in dilute solution. Proper comparisons between the BD simulation results and the experimental data for treated SWNT dilute suspensions confirm the consistency of the physical model mimicking the structure of a SWNT. (C) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012