Abstract. In this paper, numerical simulations are employed to study the orientation behavior of a dilute suspension of Brownian rigid disklike particles in a simple shear ow. Also, the viscoelasticity of such a suspension is analyzed by considering the stress budget of the two-phase material. A direct Monte-Carlo simulator as well as the moment approximation approaches with two di erent closure models are used to produce the data. Results are compared by available experimental and analytical data, and a very good agreement is established. After the validation of the simulators, the results are presented and discussed. Di erent P eclet numbers and shape factors of particles are considered and their e ects on various quantities are presented, e.g. particle orientations in space, viscous and elastic contributions to the non-Newtonian stress tensor, etc.