The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.