Simulations of the flow of concentrated aggregated colloidal systems, at the particulate level, are used to investigate the distribution of stresses in the shear-thinning regime. It is found that the distribution of shear stress carried by interparticle bonds decays approximately exponentially at large stresses, but with a double-exponential distribution for values of positive stress. The microstructural mechanisms associated with large stresses are manifested in clusters which dominate the positive contribution to the stress in the system. Towards the end of shear thinning the highest forces occur along bonds defining rods of particles aligned approximately along the flow-compression direction. We propose that the rheology of such systems is determined by a rupture–reformation process of these clusters of stress concentration during the flow. The aggregation forces play the role of enhancing such stress concentration by stabilizing clusters against buckling.