The rheology and microstructure of concentrated colloidal suspensions, within the shear thickening regime, are investigated using Stokesian dynamics. We consider systems stabilized by charge and/or polymer layers, at hard con volume fractions above 40%. At phi(upsilon) = 0.44, charge stabilized systems show transitions from ordered to disordered how, with only a small increase in suspension viscosity. At higher phi(upsilon), we observe larger jumps in viscosity with changes between order and disorder and vice versa. At high shear rates, interparticle gaps can become very small. This work investigates two ways in which these gaps may be controlled: by modifying the charge interaction potential [Dratler et al. (1997)], or by including a model for the presence of a polymer brush [Potanin and Russel (1995)]. The thickening observed is dependent on the gaps of closest approach of particles, but only weakly for hard sphere lubrication forces. Strong thickening is only observed with the presence of an enhanced lubricating force, in this article that due to a polymer coat. Models with polymer coats give examples of strong thickening within the disordered branch of flow. The effects of the number of particles used within these systems, the geometry of the computational box, and whether the simulation is two or three dimensional, can have a profound effect on the microstructure. (C) 2000 The Society of Rheology. [S0148-6055(00)00301-1].