We describe a constitutive model for monodispersed concentrated suspensions of spheres at high volume fractions. In this model the motion of a pair of generic spheres is represented by that of a pair of force-free and torque-free spheres tumbling along with the flow. The interaction with the surrounding spheres is modelled by an anisotropic diffusion process. Viscometric and elongational properties of the model are obtained by a Brownian dynamic simulation.